Sorry to drag this up again, but I’m having the same problem.
I have a program sending various requests to the REST API for several Twitter Users. It can run without problem for hours or even days but then starts having all the requests time out. As soon as the first request times out, they all do until I stop the program.
It’s set up to stay within the API limits, and any time it does exceed a limit, the appropriate error message is received and it backs off, so it doesn’t appear to be a rate limit.
I’ve currently done nothing to try and get around this (by spacing requests out beyond the API limits); is there any official guidance from Twitter for dealing with this?