Extensions disappear after cache clear

OC 3.0.3.2
I'm searched fairly broad and cannot seem to find any info, so please forgive me if I missed a thread

My sites are giving me fits with extensions. I can install a clean OC site, do some basic things like currency, localization type things and even add product. But it seems no extensions will work. They will show up sometimes, but once I clear the cache they simply disappear. Extensions that install as a module or the like work fine.

As a test I setup a totally fresh copy of OC3 and installed one extension. It showed up, then went and allowed user rights to it, refreshed the cache and it went away. I uninstalled and reinstalled and it simply won't come back. Am I simply not looking for the issue in the proper direction?

Have you tried reinstalling the same extensions or have you also tried with other extensions as well noticing the same behavior?