See elaborate description, dumps and discussion at:
http://stackoverflow.com/questions/10732940/git-operations-occasionally-hang-in-jenkins-on-windows

Basically, there is a Jenkins environment with some jobs based on GIT with periodic polling.
Each of the main GIT operations in the system (periodic polling, the pull at the beginning of a job, and the tag push at the end of a job) all sometimes hang, causing builds not to happen.

I suspect that the GIT plugin is holding handles to some GIT internal files, and this locks out the GIT command-line program and causes it to hang at the beginning of a run.
This suspicion is based on a different issue I encountered - I could not wipe the workspace for one of the jobs because a GIT pack file was locked. It turns out that the process locking the file was Tomcat itself and not the GIT process as I expected.