diff --git a/changelog.d/10400.bugfix b/changelog.d/10400.bugfix
new file mode 100644
index 000000000000..bfebed8d29df
--- /dev/null
+++ b/changelog.d/10400.bugfix
@@ -0,0 +1 @@
+Fix a number of logged errors caused by remote servers being down.
diff --git a/synapse/handlers/directory.py b/synapse/handlers/directory.py
index 4064a2b85913..06d7012bac2f 100644
--- a/synapse/handlers/directory.py
+++ b/synapse/handlers/directory.py
@@ -22,6 +22,7 @@
     CodeMessageException,
     Codes,
     NotFoundError,
+    RequestSendFailed,
     ShadowBanError,
     StoreError,
     SynapseError,
@@ -252,12 +253,14 @@ async def get_association(self, room_alias: RoomAlias) -> JsonDict:
                     retry_on_dns_fail=False,
                     ignore_backoff=True,
                 )
+            except RequestSendFailed:
+                raise SynapseError(502, "Failed to fetch alias")
             except CodeMessageException as e:
                 logging.warning("Error retrieving alias")
                 if e.code == 404:
                     fed_result = None
                 else:
-                    raise
+                    raise SynapseError(502, "Failed to fetch alias")
 
             if fed_result and "room_id" in fed_result and "servers" in fed_result:
                 room_id = fed_result["room_id"]
diff --git a/synapse/handlers/federation.py b/synapse/handlers/federation.py
index 991ec9919a95..0209aee186fa 100644
--- a/synapse/handlers/federation.py
+++ b/synapse/handlers/federation.py
@@ -1414,12 +1414,15 @@ async def send_invite(self, target_host: str, event: EventBase) -> EventBase:
 
         Invites must be signed by the invitee's server before distribution.
         """
-        pdu = await self.federation_client.send_invite(
-            destination=target_host,
-            room_id=event.room_id,
-            event_id=event.event_id,
-            pdu=event,
-        )
+        try:
+            pdu = await self.federation_client.send_invite(
+                destination=target_host,
+                room_id=event.room_id,
+                event_id=event.event_id,
+                pdu=event,
+            )
+        except RequestSendFailed:
+            raise SynapseError(502, f"Can't connect to server {target_host}")
 
         return pdu
 
@@ -3031,9 +3034,13 @@ async def exchange_third_party_invite(
             await member_handler.send_membership_event(None, event, context)
         else:
             destinations = {x.split(":", 1)[-1] for x in (sender_user_id, room_id)}
-            await self.federation_client.forward_third_party_invite(
-                destinations, room_id, event_dict
-            )
+
+            try:
+                await self.federation_client.forward_third_party_invite(
+                    destinations, room_id, event_dict
+                )
+            except (RequestSendFailed, HttpResponseException):
+                raise SynapseError(502, "Failed to forward third party invite")
 
     async def on_exchange_third_party_invite_request(
         self, event_dict: JsonDict
diff --git a/synapse/handlers/room_list.py b/synapse/handlers/room_list.py
index 5e3ef7ce3a72..c6bfa5451f37 100644
--- a/synapse/handlers/room_list.py
+++ b/synapse/handlers/room_list.py
@@ -20,7 +20,12 @@
 from unpaddedbase64 import decode_base64, encode_base64
 
 from synapse.api.constants import EventTypes, HistoryVisibility, JoinRules
-from synapse.api.errors import Codes, HttpResponseException
+from synapse.api.errors import (
+    Codes,
+    HttpResponseException,
+    RequestSendFailed,
+    SynapseError,
+)
 from synapse.types import JsonDict, ThirdPartyInstanceID
 from synapse.util.caches.descriptors import cached
 from synapse.util.caches.response_cache import ResponseCache
@@ -417,14 +422,17 @@ async def _get_remote_list_cached(
         repl_layer = self.hs.get_federation_client()
         if search_filter:
             # We can't cache when asking for search
-            return await repl_layer.get_public_rooms(
-                server_name,
-                limit=limit,
-                since_token=since_token,
-                search_filter=search_filter,
-                include_all_networks=include_all_networks,
-                third_party_instance_id=third_party_instance_id,
-            )
+            try:
+                return await repl_layer.get_public_rooms(
+                    server_name,
+                    limit=limit,
+                    since_token=since_token,
+                    search_filter=search_filter,
+                    include_all_networks=include_all_networks,
+                    third_party_instance_id=third_party_instance_id,
+                )
+            except (RequestSendFailed, HttpResponseException):
+                raise SynapseError(502, "Failed to fetch room list")
 
         key = (
             server_name,
diff --git a/synapse/http/matrixfederationclient.py b/synapse/http/matrixfederationclient.py
index b8849c0150ae..3bace2c965f3 100644
--- a/synapse/http/matrixfederationclient.py
+++ b/synapse/http/matrixfederationclient.py
@@ -43,6 +43,7 @@
 from twisted.internet.error import DNSLookupError
 from twisted.internet.interfaces import IReactorTime
 from twisted.internet.task import _EPSILON, Cooperator
+from twisted.web.client import ResponseFailed
 from twisted.web.http_headers import Headers
 from twisted.web.iweb import IBodyProducer, IResponse
 
@@ -262,6 +263,15 @@ async def _handle_response(
             request.uri.decode("ascii"),
         )
         raise RequestSendFailed(e, can_retry=True) from e
+    except ResponseFailed as e:
+        logger.warning(
+            "{%s} [%s] Failed to read response - %s %s",
+            request.txn_id,
+            request.destination,
+            request.method,
+            request.uri.decode("ascii"),
+        )
+        raise RequestSendFailed(e, can_retry=True) from e
     except Exception as e:
         logger.warning(
             "{%s} [%s] Error reading response %s %s: %s",
@@ -1137,6 +1147,24 @@ async def get_file(
                 msg,
             )
             raise SynapseError(502, msg, Codes.TOO_LARGE)
+        except defer.TimeoutError as e:
+            logger.warning(
+                "{%s} [%s] Timed out reading response - %s %s",
+                request.txn_id,
+                request.destination,
+                request.method,
+                request.uri.decode("ascii"),
+            )
+            raise RequestSendFailed(e, can_retry=True) from e
+        except ResponseFailed as e:
+            logger.warning(
+                "{%s} [%s] Failed to read response - %s %s",
+                request.txn_id,
+                request.destination,
+                request.method,
+                request.uri.decode("ascii"),
+            )
+            raise RequestSendFailed(e, can_retry=True) from e
         except Exception as e:
             logger.warning(
                 "{%s} [%s] Error reading response: %s",