I have the same problem with a Garmin strap...
The strap is several years old, that the problem?
I have found the problem is that the watch by default will connect to the external HRM via ANT+ and will also search bluetooth as well. I found that a 3rd party app on my phone was trying to connect to the external HRM sensor via bluetooth and as you can only have one bluetooth connection at the same time and this was kicking of the sensor from the watch. Then when the watch tried to reconnect to the sensor (via bluetooth) it would then also kick off the sensor from the third party app on the phone and then disconnect from the ANT+ on the watch because a bluetooth connection had been found to the sensor from the watch instead. Think of it like apps on your phone fighting over that one bluetooth connection one gets in then the other boots it off again. The way I got round this was to switch the bluetooth to phone option off from the watch so that the watch wouldn`t try and connect to the phone apps and vice versa and this worked because the watch wasn`t sending a connection via bluetooth to the phone and the sensor was happy using the ANT+ on the watch. Ive tried it twice so far and the watch hasnt reported any drop offs or disconnections from the external sensor. You will just need to switch the watch bluetooth back on when finished to sync up with garmin connect. Hope this helps. It seems that the vivoactive 3 wants to connect to an external HRM via bluetooth even when its got a connection to the ANT+ on the watch also, not sure why this is needed surely you would think Garmin would program the watch not to connect to external HRM via bluetooth if an established connection has been achieved through the default ANT+ on the device? then this would allow one third party app on your phone to at least connect to the bluetooth without disturbing the watch. Hope this is useful
I'm having the same issue with a brand new vivoaactive 4 and a brand new Garmin chest strap. Turning off Bluetooth on the watch has made no difference. I made sure my software was updated and did a factory reset on the watch and had the same problem of disconnection whether I do antenna or Bluetooth connection. Looks like our geniuses at Garmin have done nothing to solve this problem. I'm going to return both items since the wrist heart rate isn't accurate enough for my workouts.
I am not sure what the issue is. I have a Fitcent CL820W and it is connected over ANT with the bluetooth function enabled on phone and watch, never have dropouts at all and I think the watch pairs with only one sensor at a time (had a situation where I had 2 ANT/BLE sensors active simultaneously (one to my phone, one to the watch) and both worked without any glitches.