You would get a more useful response if you could update your question with details of the version of EE you are using, and the versions of the various add-ons that you think are involved.
Unpicking what is going on is likely more complex than can be addressed in this kind of forum, but there may be some steps you can take that will help you narrow down where the issues are arising.
It is unlikely that the CS / JS minimisation, or the AWS / CE Image stuff will be causing the symptoms you describe, so of the add-ons listed it would certainly be right to start by looking at CE-Cache.
CE-Cache is / was a good caching solution for EE2 / EE3 sites: the developer doesn't seem to support it any more, and while it works sort-of with later versions of EE, it is not able to support / cache pages that use newer features of the system. CE-Cache has two modes of working - it can cache bits of pages quite well (so you can cache part of a page and leave the rest to be built on each call to the template), and it also supports static-caching of whole pages (through the CE-Static Cache). You can mix / match the different kinds of caching within a site (so some pages have none, some have template element caching, and some static cached versions of the whole page). CE-Cache also has quite flexible cache-busting options too - so in theory you can ensure that a change to content triggers a cache bust of the affected pages.
My guess is that either the cache-busting configuration is not set correctly (maybe some other bits of the site design have been changed and the cache-busting rules not updated), or changes on your server are messing things up (to get maximum performance, CE-Cache's static cache pages are accessed directly by your server via .htaccess rules, rather than going through EE processing).
So to check this, find the part of the CE Cache controls that lets you nuke the cache, and when someone does one of the broken updates, try manually clearing the cache after they save their edit and see if the edit appears on the published site. (I'm guessing that this is the issue, rather than the change not actually being saved to the EE database). If it does, then probably you just need to work out what has been broken in your CE-Cache configuration and fix it. If it does not help, then probably it is something else...
Hope that helps. If you can post some environmental information and details of what happens when you start manually clearing the cache, maybe the good bods here can steer you closer to a solution.