i5 and i7 X220, i5 and i7 T420, and quad-core i7 W520.
All are 100% stable and run for days on end without a problem with Ubuntu, Pop OS, FreeBSD, and most other things.
I think you may have hardware problems.
Have you tried running Linux with a lightweight X11 window manager? Should be leaner on that T420 and a more forward-looking track for reviving old hardware. Are you even able to get latest Windows Update security patches for that device? Seems relevant for the use-case.