I've sometimes been chucked directly into the XMB after Mock Battles, though I can easily get back into the game, but after a Mock Battle I get chucked again. Didn't experience this this morning when I was sparring with Doc though, weirdly.

Ya, I think it depends on the connections between certain players. Happens to me quite regularly too. =/

I did two invasion missions yesterday with team members and got booted from the servers right after I left the sortie team. I had to reconnect.

Has this happened to anyone else?

Ya, it happens to me too, but usually after mock battles. I suspect it's a bad connection between 2 guys.