There's a bug that's been happening for a long time: When bluetooth is turned on (on the Android device) and the Edge device is not available, Garmin Connect will show a notification and vibrate the device every few minutes unless bluetooth is turned off. I found no setting to turn this off.
Same Problem here. The only thing that helps is a phone-reboot. I think it has something to do with my fitbit. Do you have any other devices connected by Bluetooth LE?
Had same problem after my Galaxy s5 updated to Android 5. Contacted Garmin who are looking in to it after offering following fix "We would like to have you turn off notifications from Garmin Connect Mobile. This will not effect your Smart notifications, but this should stop the Bluetooth Troubleshooting alerts. To do this, got to your phone settings via Android menu, go to your application manager, select Garmin Connect Mobile, then select the check mark next to show notifications. Please reply to this email if this stops the Bluetooth troubleshooting alerts"