Missy,
I'm not trying to "speak down" to you, but simply explain the issue regarding leos and their tails as best I can, so please bare with me...
A Leo *can* lose it's tail quite easilly. The reason so many pet-store leo's have stumpy tails is because they are kept in overcrowded conditions and so not only are the bigger leo's nipping the little ones, but they are ALL stressed out. I'm sure someone will correct me if there is a more expert voice in the croud, but I think that most accidental tail losses in lizards are a COMBINATION of environmental stress in conjunction with the other helpful conditions, such as responding to a fight/flight instinct at the same time a human is trying to keep them from sailing to the floor. Great conditions to lose a tail in: stress, running in great fear, and something grabs it by it's tail. One of the main reasons lizards HAVE tails is for self defense. Almost all lizards can lose their tails without suffering greatly.
Honestly, though - as long as you are careful you don't have to worry too hard that you're going to make your leo drop it's tail by handling it once in a while. The skin of a leo, as with many geckos, is also quite tender. A bad experience handling a leo would be at least as likely to result in a serious skin injury as a harless loss of the tail. So the message I'm trying to communicate is to be cautios and responsible when you handle your leo:
1. Do not hold your leo standing over an open floor; be seated or at a table (seated on the floor might be best) so that if the leo gets out of your grasp and falls that it's not going to be falling a great height.
2. In the event that your leo jumps out of your hands, you should be in an area where the critter can't hide. Not only is this helpful after the fact, but it will make YOU more relaxed if it makes a sudden move, thus helping you NOT grab it by it's tail.
3. The "together time" should be fun for both you AND your leo; try to pay attention to it's behaviour, and understand it's personality - they are all unique. If your leo seems more stressed than usual, maybe it'd be good to let them have some quiet time and try visiting again the next day.
If you and your leo are both calm while handling, that is the best situation. Until your leo is near adulthood I'd also be cautious about getting her out to show or share with friends. The extra noise and smells and movements will compound any stress she (or he) is experiencing.
The line Rich quotes IS pretty funny to anyone who's owned a leo for any length of time, but until you know any given leo that you make your pet I would excersize as much caution as feasible while handling, nevertheless.
In summary, leo's are the least "flighty" small lizard I can think of, but they are still prone to occasions of flightfulness, if you will. And they have just as much ability to auto-detach their tail as most other lizards, it's just that since they are more mellow it's not a real problem for the careful herper. So, please - don't get too worried, but remember that no matter how good a "parent" you are to your leo they might still lose their tail, and if they do it probably isn't the end of the world.
(You'd want to take it to your vet though, or at the very least dab a touch of neosporin on the stub (just once should do) to help limit the potential of infection; you'd also want to move the leo to a paper substrate for at least a week or two - again to limit the potential for any infection to set in.
I hope you and your leo have a long and happy life together!
^Curtis