You do need Audio for VATSIM to talk on the radio. But first, you’ll need to resolve the disconnection problem. If I remember correctly, VATSIM does display a message on why it disconnects: e.g. invalid login password, particular server unavailable, unacceptable/duplicate aircraft call sign etc. Hopefully, you can find a clue.
After you have obtained a stable connection, then…
1) Install Audio for VATSIM.
2) Find a location in the world where there is a current live ATC service available. You can install VATSpy, for example to see where services are staffed. Position your aircraft at a gate on one such airport.
3) Find and tune the COM frequency for that ATC. VATSpy also has info on that.
4) Connect with Audio for VATSIM; and ask the ATC for a “radio check”.
Good luck!