diff --git a/src/replit_river/v2/session.py b/src/replit_river/v2/session.py
index aeae6cfd..9d8ce129 100644
--- a/src/replit_river/v2/session.py
+++ b/src/replit_river/v2/session.py
@@ -287,7 +287,7 @@ def unbind_connecting_task() -> None:
             else:
                 logger.debug("unbind_connecting_task failed, id did not match")
 
-        if not self._connecting_task:
+        if not self._connecting_task or self._connecting_task.done():
             self._connecting_task = asyncio.create_task(
                 _do_ensure_connected(
                     transport_options=self._transport_options,
@@ -308,9 +308,16 @@ def unbind_connecting_task() -> None:
                 )
             )
 
-        await self._connecting_task
+        try:
+            await self._connecting_task
+        except asyncio.CancelledError:
+            pass
+
         if self._terminating_task:
-            await self._terminating_task
+            try:
+                await self._terminating_task
+            except asyncio.CancelledError:
+                pass
 
     def is_terminal(self) -> bool:
         """
@@ -403,7 +410,10 @@ async def close(
                     "seconds to close, leaking",
                 )
             return
-        await self._close_internal(reason)
+        try:
+            await self._close_internal(reason)
+        except asyncio.CancelledError:
+            pass
 
     def _close_internal_nowait(self, reason: Exception | None = None) -> None:
         """
@@ -501,10 +511,9 @@ async def do_close() -> None:
             # This will get us GC'd, so this should be the last thing.
             self._close_session_callback(self)
 
-        if self._terminating_task:
-            return self._terminating_task
+        if not self._terminating_task:
+            self._terminating_task = asyncio.create_task(do_close())
 
-        self._terminating_task = asyncio.create_task(do_close())
         return self._terminating_task
 
     def _start_buffered_message_sender(