I would check the ephemeral port range, maybe something/somebody could have changed that:
https://blogs.technet.microsoft.com/clinth/2013/08/09/detecting-ephemeral-port-exhaustion/
The standard range of 16.000 should be more than enough for Lansweeper operation, but that depends on your setup, of course... on my setup, with ~9000 machines and a single server, I have 180 connections open right now, not running any schedule scans...
If you want a GUI tool, you have TCPView, but that is getting a little old :
https://docs.microsoft.com/pt-pt/sysinternals/downloads/tcpview
This will shown active TCP/UDP connections, but that error may (*MAY*) indicate another issue...