I've seen them come off in the warm up pen, but luckily never in a class. Never had a tail come out myself though. I'm a pro at putting in the fake tails.
I personally prefer the double loop attachment. The way I attach tails, there is NO chance of that tail coming out until I take it out. First, I make two braids. Then, I "string" the braids through the two loops. Use those braid, and take two more sections of hair for each braid, and braid those. Then, use those two braids, and a section of hair from the fakie, and braid those together. I'm sure it would make a lot more sense with pictures! Basically, the trick is lots of braids.
Oh! And a hair clip. You'll want a really big hair clip to clip half of the tail up so that it's out of your way while you're putting it in.