I would suspect it's your power settings. If it's set to turn the screen off before sleep, Spotify will continue to play. If it sleeps at the same time the screen turns off, Spotify will stop.
You can change your power settings to turn the screen off after 5ish minutes and go to sleep after an hour. I find that I do something at least once an hour when listening to Spotify so it doesn't shut off.
Sadly, my first instinct is to reply "yea, buy an iPad". Seriously, if Spotify pushed a Windows app I could probably go cold turkey on one device [well, ok. . add MK X to that and THEN I could go cold turkey]
In lieu of Spotify, I use TuneIn Radio for those times when I wanna just let it play in the background.
TuneIn works great on my Android phone but my problem is that it DOES keep running, even if I try to stop it it doesn't really close unless I kill the process. That and Waze can both cause a big drain.