ESI Problems

Hello Staff 🙂
I have a website where I use plugin download after email (https://wordpress.org/plugins/download-after-email/). I collected all nonces:
dae_download
dae_admin
dae_update

and enabled ESI
https://monosnap.com/file/AEWWdUGQrwSLiDJbkq7C0hvYpXHrUZ

However, I’m still experiencing issues after certain random time. Sometimes it’s 24h, sometimes, few days. I even set auto-purge for those pages, yet still, I’m experiencing sometimes 403 errors.
Any other clues?

P.S. Of course, all is fine when I refresh the cache. Then it happens again after random time.
Best,

The page I need help with: [log in to see the link]