diff --git a/telethon/client/downloads.py b/telethon/client/downloads.py
index b52e2fa5..22a7997d 100644
--- a/telethon/client/downloads.py
+++ b/telethon/client/downloads.py
@@ -202,6 +202,7 @@ class DownloadMethods(UserMethods):
 
         # The used sender will change if ``FileMigrateError`` occurs
         sender = self._sender
+        exported = False
         input_location = utils.get_input_location(input_location)
 
         __log__.info('Downloading file in chunks of %d bytes', part_size)
@@ -217,7 +218,8 @@ class DownloadMethods(UserMethods):
                         raise NotImplementedError
                 except errors.FileMigrateError as e:
                     __log__.info('File lives in another DC')
-                    sender = self._get_exported_sender(e.new_dc)
+                    sender = self._borrow_exported_sender(e.new_dc)
+                    exported = True
                     continue
 
                 offset += part_size
@@ -233,7 +235,9 @@ class DownloadMethods(UserMethods):
                 if progress_callback:
                     progress_callback(f.tell(), file_size)
         finally:
-            if sender != self._sender:
+            if exported:
+                self._return_exported_sender(sender)
+            elif sender != self._sender:
                 sender.disconnect()
             if isinstance(file, str) or in_memory:
                 f.close()
diff --git a/telethon/client/messages.py b/telethon/client/messages.py
index 1d552277..f47cd25e 100644
--- a/telethon/client/messages.py
+++ b/telethon/client/messages.py
@@ -1,7 +1,7 @@
 import asyncio
 import itertools
 import logging
-import warnings
+import time
 from collections import UserList
 
 from async_generator import async_generator, yield_
@@ -188,7 +188,7 @@ class MessageMethods(UploadMethods, MessageParseMethods):
         last_id = float('inf')
         batch_size = min(max(batch_size, 1), 100)
         while have < limit:
-            start = asyncio.get_event_loop().time()
+            start = time.time()
             # Telegram has a hard limit of 100
             request.limit = min(limit - have, batch_size)
             r = self(request)
@@ -242,9 +242,8 @@ class MessageMethods(UploadMethods, MessageParseMethods):
                 else:
                     request.max_date = last_message.date
 
-            now = asyncio.get_event_loop().time()
             asyncio.sleep(
-                max(wait_time - (now - start), 0), loop=self._loop)
+                max(wait_time - (time.time() - start), 0), loop=self._loop)
 
     def get_messages(self, *args, **kwargs):
         """
diff --git a/telethon/client/telegrambaseclient.py b/telethon/client/telegrambaseclient.py
index bb5fa3f7..4c64334e 100644
--- a/telethon/client/telegrambaseclient.py
+++ b/telethon/client/telegrambaseclient.py
@@ -67,9 +67,7 @@ class TelegramBaseClient(abc.ABC):
 
         timeout (`int` | `float` | `timedelta`, optional):
             The timeout to be used when connecting, sending and receiving
-            responses from the network. This is **not** the timeout to
-            be used when ``await``'ing for invoked requests, and you
-            should use ``asyncio.wait`` or ``asyncio.wait_for`` for that.
+            responses from the network.
 
         request_retries (`int`, optional):
             How many times a request should be retried. Request are retried
@@ -211,9 +209,11 @@ class TelegramBaseClient(abc.ABC):
             auto_reconnect_callback=self._handle_auto_reconnect
         )
 
-        # Cache :tl:`ExportedAuthorization` as ``dc_id: MTProtoState``
-        # to easily import them when getting an exported sender.
-        self._exported_auths = {}
+        # Cache ``{dc_id: (n, MTProtoSender)}`` for all borrowed senders,
+        # being ``n`` the amount of borrows a given sender has; once ``n``
+        # reaches ``0`` it should be disconnected and removed.
+        self._borrowed_senders = {}
+        self._borrow_sender_lock = threading.Lock()
 
         # Save whether the user is authorized here (a.k.a. logged in)
         self._authorized = None  # None = We don't know yet
@@ -355,36 +355,65 @@ class TelegramBaseClient(abc.ABC):
             and bool(dc.ipv6) == self._use_ipv6 and bool(dc.cdn) == cdn
         )
 
-    def _get_exported_sender(self, dc_id):
+    def _create_exported_sender(self, dc_id):
         """
-        Returns a cached `MTProtoSender` for the given `dc_id`, or creates
-        a new one if it doesn't exist yet, and imports a freshly exported
-        authorization key for it to be usable.
+        Creates a new exported `MTProtoSender` for the given `dc_id` and
+        returns it. This method should be used by `_borrow_exported_sender`.
         """
         # Thanks badoualy/kotlogram on /telegram/api/DefaultTelegramClient.kt
         # for clearly showing how to export the authorization
-        auth = self._exported_auths.get(dc_id)
         dc = self._get_dc(dc_id)
-        state = MTProtoState(auth)
+        state = MTProtoState(None)
         # Can't reuse self._sender._connection as it has its own seqno.
         #
         # If one were to do that, Telegram would reset the connection
         # with no further clues.
         sender = MTProtoSender(state, self._connection.clone())
         sender.connect(dc.ip_address, dc.port)
-        if not auth:
-            __log__.info('Exporting authorization for data center %s', dc)
-            auth = self(functions.auth.ExportAuthorizationRequest(dc_id))
-            req = self._init_with(functions.auth.ImportAuthorizationRequest(
-                id=auth.id, bytes=auth.bytes
-            ))
-            sender.send(req)
-            self._exported_auths[dc_id] = sender.state.auth_key
+        __log__.info('Exporting authorization for data center %s', dc)
+        auth = self(functions.auth.ExportAuthorizationRequest(dc_id))
+        req = self._init_with(functions.auth.ImportAuthorizationRequest(
+            id=auth.id, bytes=auth.bytes
+        ))
+        sender.send(req)
+        return sender
+
+    def _borrow_exported_sender(self, dc_id):
+        """
+        Borrows a connected `MTProtoSender` for the given `dc_id`.
+        If it's not cached, creates a new one if it doesn't exist yet,
+        and imports a freshly exported authorization key for it to be usable.
+
+        Once its job is over it should be `_return_exported_sender`.
+        """
+        with self._borrow_sender_lock:
+            n, sender = self._borrowed_senders.get(dc_id, (0, None))
+            if not sender:
+                sender = self._create_exported_sender(dc_id)
+                sender.dc_id = dc_id
+
+            self._borrowed_senders[dc_id] = (n + 1, sender)
 
         return sender
 
+    def _return_exported_sender(self, sender):
+        """
+        Returns a borrowed exported sender. If all borrows have
+        been returned, the sender is cleanly disconnected.
+        """
+        with self._borrow_sender_lock:
+            dc_id = sender.dc_id
+            n, _ = self._borrowed_senders[dc_id]
+            n -= 1
+            if n > 0:
+                self._borrowed_senders[dc_id] = (n, sender)
+            else:
+                __log__.info('Disconnecting borrowed sender for DC %d', dc_id)
+                sender.disconnect()
+                del self._borrowed_senders[dc_id]
+
     def _get_cdn_client(self, cdn_redirect):
-        """Similar to ._get_exported_client, but for CDNs"""
+        """Similar to ._borrow_exported_client, but for CDNs"""
         # TODO Implement
         raise NotImplementedError
         session = self._exported_sessions.get(cdn_redirect.dc_id)
diff --git a/telethon/network/mtprotoplainsender.py b/telethon/network/mtprotoplainsender.py
index 71ea99eb..3a71aaa5 100644
--- a/telethon/network/mtprotoplainsender.py
+++ b/telethon/network/mtprotoplainsender.py
@@ -39,10 +39,15 @@ class MTProtoPlainSender:
             raise BrokenAuthKeyError()
 
         with BinaryReader(body) as reader:
-            assert reader.read_long() == 0  # auth_key_id
-            assert reader.read_long() > msg_id  # msg_id
-            assert reader.read_int()  # length
+            assert reader.read_long() == 0, 'Bad auth_key_id'  # auth_key_id
 
+            assert reader.read_long() != 0,  'Bad msg_id'  # msg_id
+            # ^ We should make sure that the read ``msg_id`` is greater
+            # than our own ``msg_id``. However, under some circumstances
+            # (bad system clock/working behind proxies) this seems to not
+            # be the case, which would cause endless assertion errors.
+
+            assert reader.read_int() > 0,  'Bad length'  # length
             # We could read length bytes and use those in a new reader to read
             # the next TLObject without including the padding, but since the
             # reader isn't used for anything else after this, it's unnecessary.