Could this be a hardware issue? I have the same issue on my macbook. For me, the headphone jack is **bleep** up, so a little movement of the headphones will play or pause whatever I'm listening to. Do you usually listen to your music with wired headphones?
Hmm, alright. Does this only happen with Spotify? Like if you watch a video on Youtube or Netflix or whatever, will it pause randomly then, too? If so, it's probably an issue with you device. If it only happens with Spotify, I would recommend trying a clean reinstall and see if that helps.