In my experience Starman is highly unstable. It might have been a bad combination of environment issues and older Perl but I got hangs and segfaults all the time and had to ditch it.

uWSGI RFC:SHOULD be the best, easily. You might review the docs to see your usage is cromulent and update to the latest version for good measure. I run a couple of applications on it, not high traffic but up to many thousands of views a day, most pages dynamic, and I've never had any issues whatsoever. I've stress tested it out to high traffic levels with excellent results. It runs from server reboot to reboot without any attention. Longest stretch I've left it running is a year-ish. If you're having trouble, especially regardless of app engine, you might have a memory leak or various other problems in your Perl or things it calls beneath.