They say it can't possibly be a server problem, since a restart always solves the problem
Sometimes my car cuts out but it starts up again when I turn the key. It can't possibly be an engine problem as the car starts up when I turn the key.
That's pretty much the same thing. I work with servers so it could be a memory issue, drive write issue, NIC issue, etc. But, having said that it possibly isn't that.
Occam razor.
You may have to remove the plugins except the protection one (as you said you need that one for your server to work). You could remove the Teleport and ABM for a 'test period'. If the server still crashes without these plugins my thoughts would go towards something dicky at the host.
It's very hard for anyone to give any help without an error log. It just ends up with a lot of "try this try that", until someone suggests a world reset (don't do that!
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