Am I barking up the wrong tree or could it be that there are two different clocks (so to speak) at the server end?

Very unlikely, but not inconceivable ( virtual machines , rogue time server, broken time daemons ... )

and if there were and they were out of sync would this explain why, at my end, it randomly stops being able to find the files?

No. If it is too old, it will still be there. Chances are you have a coding error -- or doing something bizzare like keeping the config file in a temp directory which gets emptied every 2-3 days.