SIP connections no longer accepted

From time to time (after approx. every 2-10 weeks) our Asterisk stops to accept SIP requests. Existing calls are handled by the dial plan and the audio gets through, but new SIP connections time out. We had this with Asterisk 1.6.2 and unfortunately the 1.8 update has not improved things. The log file shows no error messages regarding the SIP module. What are possible causes for this? What steps can we take to debug/analyze this issue?

Deadlocks.

Comple with no optimise, and thread debugging enabled.

Run core show locks and look for cycles in the locks. If found on 1.8.7ish, also take backtraces and report on issues.asterisk.org.