Finally I got the solution. Follow these steps:
- Open the registry editor. (If you don't know how, open search Cortana and type "regedit")
- Using the folders on the left hand side, navigate to the following folder: HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Power
- Change the value of "CsEnabled" from 1 to 0
- Reboot your Surface.
- After rebooting, not only the issue of stopping playing get resolved but also you see "Power Saver" and "High Performance" options in your power options.
I can confirm, this does not help. When I follow that, the moment I switch off my Surface Pro 3, it stops working and it kind of reboots. Takes the same time to get back, but it not really booted then. Basically it is worse than without these steps... :(
I googled a bit and it looks like it's a problem with the Spotify or other apps, which are not perfectly adjusted to the Windows 10.
What surprises me is the fact that I used to not have a problem earlier... I was using Windows 10 and Spotify and recently set up my system again. I don't know, if I had changed some settings earlier and if so, which ones.