Might there be too heavy a load on your ArcGIS Server, as you say you have many services. I use free-software called 123LogAnalyzer to get me a rough idea on how often my AGS services are being hit.I'm not sure if the 123LogAnalyzer will be able to determine too heavy a load, but can you shut down some services (not sure if this is possible in your production environment) and see if the problem still continues.
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