I have no problems with Mixxx in that regard. I run it on Linux and for me it is rock solid. It can't help if your computer crashes though.

I used to use mpd for a while which automatically continues playing where it left off after a reboot.

What I learned from that phase is that the music I enjoy in the evening is rarely the same I like blasted in my ears mid-song at full volume in the morning. Terribly annoying feature, will not use again.