I briefly get the login screen when starting the app now. It proceeds to the "contacting the car" page after a few seconds, but it still looks like I'd need to login again. Just long enough for me to think "Oh, what now?" Didn't used to do this. I still almost always have to back out and restart the app in order to successfully connect though. I usually give it 10 seconds (occasionally, it does do it on the first try) and, if no connection, back out and try again.
Try resetting your password in myTesla. That worked for me.