diff --git a/gunicorn/workers/base_async.py b/gunicorn/workers/base_async.py
index 6a79d7ed0..9f648a17d 100644
--- a/gunicorn/workers/base_async.py
+++ b/gunicorn/workers/base_async.py
@@ -36,7 +36,8 @@ def handle(self, listener, client, addr):
             parser = http.RequestParser(self.cfg, client, addr)
             try:
                 listener_name = listener.getsockname()
-                if not self.cfg.keepalive:
+                # do not allow keepalive if the worker is about to be restarted
+                if not self.cfg.keepalive or not self.alive:
                     req = next(parser)
                     self.handle_request(listener_name, req, client, addr)
                 else:
diff --git a/gunicorn/workers/ggevent.py b/gunicorn/workers/ggevent.py
index 2125a32d0..844e196a7 100644
--- a/gunicorn/workers/ggevent.py
+++ b/gunicorn/workers/ggevent.py
@@ -87,6 +87,11 @@ def run(self):
             self.notify()
             gevent.sleep(1.0)
 
+        # wait for the keepalive period to end before stopping the acceptance of new requests
+        ts = time.time()
+        while time.time() - ts <= self.cfg.keepalive:
+            gevent.sleep(1.0)
+
         try:
             # Stop accepting requests
             for server in servers: