Why do we see a black screen popup that says connecting ... in Avlytics Server ? 

This screen indicates a vpn disconnection. 

If the avlytics server pc loses internet connectivity for event a second, it will cause the vpn connection to disconnect.
The black screen is a service built into avtass software that will attempt to automatically reconnect the vpn connection.

This service will attempt reconnect up to 20 times before it will stop trying.

if the internet connection is not reestablished within these 20 attempts the black screen will remain open indicating that the machine is not connected to the vpn server. 

In these cases , simply close the Avtass software and black screen service. 

Reconnect VPN  and open Avtass.
everything will go back to normal.