A few times now when over a dead friend I have gotten the "Help Me" prompt. Pressing A then restores some of their help and they get back in the fight. There does not seem to be any rhyme or reason to why and how it shows up. So what determines if i can actually revive somebody or not?
You should be able to revive someone if you have 3000 TP. You party members can do the same thing, but they usually use an Art, blowing their chance to revive you. You can send a battle command to your party to build the tension, which will help but doesn't by any means guarantee they'll save the TP required to revive you.