Thank you for your post.
How much memory is in the Mac Mini? Do you notice how much memory is being used when the issue occurs? After restart, see how much memory is running, and the next time this issue occurs, check the memory again.
How many clients are accessing the database (FileMaker Pro/Go/WebDirect/Custom Web Publishing/etc.)?
Does Event.log show anything at the time this issue occurs? Access.log?
Do you notice anything in the Admin Console when the issue occurs? For example, is the Web Publishing Engine still running?
Any other information you can provide may be helpful in narrowing down the possible cause.
Thanks for the followup.
I have learned that there was an issue already recorded regarding this server behavior.
We have installed the latest FM Server v14.0.4a and are awaiting some time to see if the problem was resolved with the latest updates.