If the issue is consistent across servers, then perhaps the problem could be due to the code you use.
Maybe you are looping over code and performing some kind of break, or rand operation? This could allow for a ‘sporadic’ appearance if not coded perfectly.
I would definitely setup a local version of your site using MAMP or similar to test on perfect server situations.
Also, try disabling all plugins on the local site. This may fix the issue, and you can then add them back in one by one until you hit the problem.
Maybe also do some debugging with ACF’s function
get_field and WP’s functions
get_postmeta to compare the differences
Welcome to the Advanced Custom Fields community forum.
Browse through ideas, snippets of code, questions and answers between fellow ACF users
Helping others is a great way to earn karma, gain badges and help ACF development!