This is a common occurance in The Big Dig with the added bonus prize of after getting auto kicked from team, you are beamed off the planet and can not rejoin the FA at all until your previous team either quits or completes the mission. The bug is extremely old and is yet still around. Just another case of me not recommending you holding your breath to see it fixed.
I have had it happen in the mirror event, luckilly you don't get kicked out but it does make it a tad difficult for team coordination whne ou can'tuse team chat. It also makes it difficult to see who needs your help most as the team members disappear for obvious reasons.
You CAN recreate a team again as long as you are all the same faction.
Happens a bit in STF and I've managed to create a team again with your respective faction but am unable to invite the other faction. Good if you are all one faction, not-so-good when you're the only Klingon/Fed