If everything is fine on local, but intermittently you are getting 504s on a live webserver that does sound like a load issue. Have you looked at what traffic the site is getting? Is it possible you’re being hammered by bot traffic?
You don’t say how you are using the fields, but often if you have a bunch of custom fields, you have those custom fields because you want to be able to navigate and filter with them. If you can navigate and filter with them, you can easily end up with bots looping through your content and gobbling your server resources just by pulling stuff out of your database in every possible combination. PITA, truly.
I am not sure it’s really an ACF issue, you can get the same thing happening with tags and categories if you have enough of them. If that is the issue, then caching, redis, and cloudflare bot protection might help.
If it’s not that, you might find WordPress Query Monitor handy – it will give you a report to show what queries are running and how slow they are.
Hope that helps. I’m not an admin, just another user!
