I do tend to run out of mana when I'm not being focused by the other team in arena. This is worst when I'm dealing with a rogue and periodically dropping consecration to try to pop him out of stealth.
Hopefully the changes in 3.1 will remove this problem and our mana will be much more stable regardless of who is being targeted. I suspect that we'll be fine so long as we aren't using consecration much or healing (which you shouldn't be doing much of anyway). I rarely need Divine Plea, but it always seems to get me through any rough spots.
BG's are a bit of a different story. I think you're always going to run out of mana there, but one of two things will happen fairly quickly. You'll either defend/take the node you're fighting at and have time to drink or you'll be dead and rez with a full mana bar anyway.