It's only happened to me once so far, and that was in my first battle. I had my two Chemists spread out on either side of the feild and then my female one got sucker punched by a Theif. At this point there is no way to revive dead characters, so she became a Leather Cap (lol that sounds like I skinned her). I was a little sad that I couldn't save her but afterwards I just switched my female Squire to a Chemist and now she's a White Mage. I haven't looked back since.

My Black Mage/Chemist died the other day, and as he was the only one able to use Pheonix Downs, I had no choice but to reset. But really If you keep your character's relatively close together and don't send one guy out on his lonesome, it's not hard to keep them alive or revive them if they die. It's all part of he strategy.