Recently in an arena match on a 2.4.3 Mangoes server, I died and the reincarnation option popped up. I was able to reincarnate but still lost the match. I wasn't wearing the Deck of Portals trinket but I do remember what I did in particular before the arena match. I can't test it right now since I patched to 3.09 WotLK but I'm pretty sure it was because of this particular action.
Anyways, here is what I did:
1) Que for arena.
2) When the que pops up to enter, I used .st. When the unstuck bar was half way done casting, I entered arena.
That was all. This was the only thing I did different in all my arena matches and it was the only arena match that I was able to reincarnate. Hope someone can test it out for me. Also, be sure that your reincarnate cooldown is refreshed before you enter arena. I'm pretty sure this works.