Frequent unpairing

Not sure whether you are not confusing the syncing / connecting with pairing - those are completely two different issues. While at failed pairing you will be requested by Garmin Connect to add or pair a device, at a lost connection, the watch will simply fail to sync, and there can be countless number of reasons for it - most of them are listed in the Sync / Connection Troubleshooting Guide, so make sure you have checked them all.

It's paring request as I need to introduce the 6 digits number after being out of range for bluetooth. The request itself is from Connect App. Also the device (Vivoactive 4s) is not listed in the bluetooth paired devices list of the phone.

Have a look at the thread Pairing with Phone does not work - specifically the last post by user 1684245 - he tells he had to remove all BT pairings from his phone (not only those for the watch), before being able to pair the watch properly. You also better do it on all devices you used to pair with the watch, and keep on only one of them at a time, when re-trying. 

And also, have a look at the the troubleshooting guide on the Support site, some hints may perhpas help in your case too:

I am getting a "Pairing Failed" message when setting up my Garmin device through the Garmin Connect App

Thank you for links.

Tried all this methods, there are no issues with paring at all as a process, it works smooth without glitches.

Steps to reproduce:

1. Have Vivoactive 4s paired and working with Connect App. In paired bluetooth device list it's registered under name Vivoactive 4s.

2. Get out of Bluetooth range for a while (usually several minutes).

3. Return back to Bluetooth range.

4. Connect App will notify me with a request of pairing the device.

5. Checking the Bluetooth paired devices will not contain the previously registered connection Vivoactive 4s.

6. Pairing by clicking on the notification that came out from Connect App and introducing the 6 digits number shown on watch will work smooth.

7. Checking the Bluetooth paired devices will contain a registered connection Vivoactive 4s.

Check out this video, and make sure you did not skip any of the steps:

Tried the steps described. Still no luck. Keeps sending paring requestest after being out of range for Bluetooth connection.