PYTHON-3468 [v3.13] Test failures in test_srv_polling.TestSrvPolling (#1073) (#1092)

.evergreen/config.yml

@@ -2927,8 +2927,8 @@ buildvariants:
 
 - matrix_name: "test-linux-enterprise-auth"
   matrix_spec:
-    platform: awslinux
-    python-version: *amazon1-pythons
+    platform: ubuntu-18.04
+    python-version: ["3.7", "3.8", "3.9", "3.10", "3.11", "pypy3.7"]
     auth: "auth"
   display_name: "Enterprise ${auth} ${platform} ${python-version}"
   tasks:

test/test_srv_polling.py

@@ -125,7 +125,14 @@ class TestSrvPolling(unittest.TestCase):
         (WAIT_TIME * 10) seconds. Also check that the resolver is called at
         least once.
         """
-        sleep(WAIT_TIME * 10)
+
+        def predicate():
+            if set(expected_nodelist) == set(self.get_nodelist(client)):
+                return pymongo.srv_resolver._SrvResolver.get_hosts_and_min_ttl.call_count >= 1
+            return False
+
+        wait_until(predicate, "Node list equals expected nodelist", timeout=100 * WAIT_TIME)
+
         nodelist = self.get_nodelist(client)
         if set(expected_nodelist) != set(nodelist):
             msg = "Client nodelist %s changed unexpectedly (expected %s)"