A very large set of OldData can take a long time to discard. While this is running, most Jenkins operations which save any data are blocked.

https://gist.github.com/recampbell/9336d3a32270e75a9333

doDiscard is synchronized and hudson.diagnosis.OldDataMonitor#remove also wants to lock OldDataMonitor. Most threads eventually lock when saving something, at least until the doDiscard eventually completes.