Hi,
I had the same problem, with a forerunner 230 but with Garmin Connect App running ,going in
Settings -- Battery -- Launch, and then set Connect to: "Manage manually" plus keep all the settings on in “Manage manually” menu
You can close the Garmin App and now the Forerunner 230 seems to keep the bluethoot active .
Hope this help
I have Mate 10 Pro, and I do not have any problems with my Garmin 5. Perhaps it should be checked whether the mobile phone software is shutting down the Connect app. On my cellphone, the setting is in: Settings -- Battery -- Launch, and then set to: "Manage manually" for Connect app.