diff --git a/.github/workflows/DocCleanup.yml b/.github/workflows/DocCleanup.yml
index 612794f06..463a5f599 100644
--- a/.github/workflows/DocCleanup.yml
+++ b/.github/workflows/DocCleanup.yml
@@ -1,24 +1,30 @@
 name: Doc Cleanup
 on:
-  push:
-    branches:
-      - gh-pages
+  # runs on the 1st day of every month at 03:00 UTC
+  schedule:
+    - cron: '0 3 1 * *'
   workflow_dispatch:
+permissions:
+  contents: write
 jobs:
   doc-cleanup:
     runs-on: ubuntu-latest
     steps:
       - name: Checkout gh-pages branch
-        uses: actions/checkout@v4
+        uses: actions/checkout@v7
         with:
           ref: gh-pages
       - name: Delete old docs
         run: |
-            keep=$(readlink stable)
+            keep="$(readlink stable)"
             git config user.name "Documenter.jl"
             git config user.email "documenter@juliadocs.github.io"
-            git rm -rf v[0-9]*.[0-9]* && git checkout HEAD -- $keep
-            if git commit -m "keep latest docs only" ; then
+            git rm -rf --ignore-unmatch "v[0-9]*.[0-9]*" "previews/*"
+            git checkout HEAD -- "$keep"
+            if git diff --cached --quiet; then
+              echo "No old docs or previews to delete"
+            else
+              git commit -m "Delete old docs and previews"
               git branch gh-pages-new $(echo "delete history" | git commit-tree HEAD^{tree})
               git push --force origin gh-pages-new:gh-pages
             fi