Jenkins was crashing on a daily basis. The problem disappears when all the Doxygen jobs were disabled. I've since uninstalled the plugin.
We have a large code base so the doxygen documentation is big. It was running as a build step to produce the doxygen docs, and then the publish doxygen option was used to provide the link.
It's not clear how this plugin works. At first I assumed it was just linking, but the url's generated seem to suggest it's copying the produced docs. I'm not sure though.
I'm sorry I can't provide more detailed information.