RESTlet Inconsistency

We have a client that has a heavily built out integration with some external systems utilizing RESTlets. They've started noticing the last couple of weeks NetSuite just isn't acknowledging calls to the RESTlets on random occasions, just returning an empty response, and nothing even gets logged in the event log. We know the calls from outside are good - we tested by creating a script on their server that just loops through a handful of hard-coded calls (so the calls wouldn't change from execution to execution) when we want to test. Sometimes the calls work fine, other times as I