diff --git a/test/functional/abc_p2p_avalanche_proof_voting.py b/test/functional/abc_p2p_avalanche_proof_voting.py
--- a/test/functional/abc_p2p_avalanche_proof_voting.py
+++ b/test/functional/abc_p2p_avalanche_proof_voting.py
@@ -20,12 +20,7 @@
     AvalancheVote,
 )
 from test_framework.test_framework import BitcoinTestFramework
-from test_framework.util import (
-    assert_equal,
-    assert_greater_than,
-    assert_raises_rpc_error,
-    try_rpc,
-)
+from test_framework.util import assert_equal, assert_raises_rpc_error, try_rpc
 from test_framework.wallet_util import bytes_to_wif
 
 QUORUM_NODE_COUNT = 16
@@ -86,6 +81,20 @@
 
         return found_hash
 
+    def can_not_find_proof_in_poll(self, hash, response):
+        # We call can_find_proof_in_poll multiple times to be sure of the
+        # outcome.
+        for _ in range(5):
+            if self.can_find_proof_in_poll(hash, response):
+                return False
+
+            # The expected poll wasn't found. Wait a little and try again.
+            time.sleep(0.5)
+
+        # After a short time, it appears that no peer is being polled for this
+        # item.
+        return True
+
     @staticmethod
     def send_proof(from_peer, proof_hex):
         proof = avalanche_proof_from_hex(proof_hex)
@@ -245,17 +254,9 @@
         self.log.info("Test the peer replacement rate limit")
 
         # Wait until proof_seq30 is finalized
-        retry = 5
-        while retry > 0:
-            try:
-                with node.assert_debug_log([f"Avalanche finalized proof {proofid_seq30:0{64}x}"]):
-                    self.wait_until(lambda: not self.can_find_proof_in_poll(
-                        proofid_seq30, response=AvalancheProofVoteResponse.ACTIVE))
-                break
-            except AssertionError:
-                retry -= 1
-
-        assert_greater_than(retry, 0)
+        with node.assert_debug_log([f"Avalanche finalized proof {proofid_seq30:0{64}x}"]):
+            self.wait_until(lambda: self.can_not_find_proof_in_poll(
+                proofid_seq30, response=AvalancheProofVoteResponse.ACTIVE))
 
         # Not enough
         assert self.conflicting_proof_cooldown < self.peer_replacement_cooldown
@@ -470,17 +471,9 @@
             proofid_seq1, response=AvalancheProofVoteResponse.UNKNOWN), timeout=10)
 
         # Wait until proof_seq1 voting goes stale
-        retry = 5
-        while retry > 0:
-            try:
-                with node.assert_debug_log([f"Avalanche stalled proof {proofid_seq1:0{64}x}"]):
-                    self.wait_until(lambda: not self.can_find_proof_in_poll(
-                        proofid_seq1, response=AvalancheProofVoteResponse.UNKNOWN), timeout=10)
-                break
-            except AssertionError:
-                retry -= 1
-
-        assert_greater_than(retry, 0)
+        with node.assert_debug_log([f"Avalanche stalled proof {proofid_seq1:0{64}x}"]):
+            self.wait_until(lambda: self.can_not_find_proof_in_poll(
+                proofid_seq1, response=AvalancheProofVoteResponse.UNKNOWN))
 
         # Verify that proof_seq2 was not replaced
         assert proofid_seq2 in get_proof_ids(node)