diff --git a/supervisor/supervisor.go b/supervisor/supervisor.go
index b2c19e79f28..3a0807bfc46 100644
--- a/supervisor/supervisor.go
+++ b/supervisor/supervisor.go
@@ -131,6 +131,7 @@ func (s *Supervisor) Run(
 	var backoffTimer <-chan time.Time
 
 	shuttingDown := false
+	gracefulShutdownC := s.gracefulShutdownC
 	for {
 		select {
 		// Context cancelled
@@ -175,8 +176,10 @@ func (s *Supervisor) Run(
 				// No more tunnels outstanding, clear backoff timer
 				backoff.SetGracePeriod()
 			}
-		case <-s.gracefulShutdownC:
+		case <-gracefulShutdownC:
 			shuttingDown = true
+			// Avoid making the loop spin while the tunnels drain.
+			gracefulShutdownC = nil
 		}
 	}
 }