I have noticed that if I press Esc to stop waiting, and go to the in-game server browser, the server I tried to join, and any other servers hosted on different ports at the same address, are not visible. However, if I close Arma and start it normally again, I can verify that the server is still working.
I have what I believe to be the same problem with Arma 2 and Operation Arrowhead (see https://dev-heaven.net/issues/41085).
Since reporting the issue in Arma 2, I have changed motherboard, CPU, RAM, and Windows version (XP -> 7), to no effect. I am still using the same ATI Radeon HD 5670. In other respects, Arma 2 and 3 both play beautifully, and I have no unusual issues joining games with the in-game server browser.