I said it last night and I'll say it again:
I got booted out of a "strike" on Division during the Boss Fight with an error, and when I logged back into I automatically got put back in.
Destiny NEEDS to add that.
Destiny also needs to hold your spot in PvP, whether it's Trials or any matchmade playlist.
Trials, that spot should be yours for the duration of that match. You should be able to rejoin so long as it's the same character (even if you pick a different character, you're missing at least 1 or 2 crucial rounds, so this part can even be debateable).
Matchmade, that spot should be yours for maybe a minute so it can't get scooped by a random so quickly.
Or, they can differentiate between leaving manually and getting kicked out, so if you left manually, your spot wouldn't be held for a minute or whatever number seems to be the best to hold it.