I have tried to recreate your issue but I could not find any direct problems between Spotify Connect and Bluetooth. But with my device I found some problems between Spotify Connect and Squeezelite. This is an occasional issue, especially with the HiFiBerry Amp+, which we are currently solving to provide the ideal transition between these two.
Please try to stop Squeezelite and Shairtunes and report back if this is solves the problem for the moment.
If not: please share your Spotify Connect debug log and tell me what kind of internet connection you are using.