It isn't just phones that do this. I'm casting to my stereo that is connected to a FireTV for the audio. Regardless of whether I launch using a phone, an iPad, or the spotify web player, it will randomly stop playing. Sometimes after a few minutes, sometimes it works for an hour or two. Spotify has a bug and there's nobody to ask to fix it.
I've also had this issue. My Fix was turning off "optimise battery usage" for Spotify. You can find this option under Apps>Spotify>Battery>Optimise battery usage. Then select all apps and search for Spotify. You have to turn this off.