diff --git a/ci_scripts/mark-pr-ready.py b/ci_scripts/mark-pr-ready.py
index 2fbee7f32682..8d44747379e6 100755
--- a/ci_scripts/mark-pr-ready.py
+++ b/ci_scripts/mark-pr-ready.py
@@ -37,13 +37,14 @@
 from dataclasses import dataclass
 
 import requests
-from github import Auth, Github
+from github import Auth, Github, GithubException
 from github.PullRequest import PullRequest
 from github.Repository import Repository
 from github.WorkflowRun import WorkflowRun
 
 REPOSITORY = "riseproject-dev/python-wheels"
 PASSING_CONCLUSIONS = {"success", "skipped"}
+MERGE_REJECTED_STATUSES = {405, 409, 422}
 
 
 def convert_to_draft(token: str, pr: PullRequest) -> None:
@@ -127,9 +128,22 @@ def sync_pull_request(
         if merge:
             actions.append("squash merge")
             if not dry_run:
-                result = pr.merge(merge_method="squash", sha=pr.head.sha)
-                if not result.merged:
-                    actions[-1] = f"merge rejected: {result.message}"
+                try:
+                    result = pr.merge(merge_method="squash", sha=pr.head.sha)
+                except GithubException as exc:
+                    # GitHub answers 405 when the PR cannot be merged (e.g. merge
+                    # conflicts), 409 when its head moved since we looked, and
+                    # 422 for other validation failures.  These affect only this
+                    # PR, so report them and carry on with the rest.
+                    if exc.status not in MERGE_REJECTED_STATUSES:
+                        raise
+                    message = (
+                        exc.data.get("message") if isinstance(exc.data, dict) else None
+                    )
+                    actions[-1] = f"merge rejected: {message or exc.status}"
+                else:
+                    if not result.merged:
+                        actions[-1] = f"merge rejected: {result.message}"
     elif not pr.draft:
         actions.append("convert to draft")
         if not dry_run: