Julie, The simple answer is you have a short some where. A few weeks ago I had to replace some wiring in my brothers home. As it turns out he had some squirrels get into the ceiling space and build a nest... the buggers chewed up a few sections of wiring all the way to bare copper.
To check this out first check ( or have your electrician) check the connections in the fixtures themselves and at the switch. If those are good you will need to look deeper.
In my brothers case we had some "clues" as he would hear noises up there now and then. This allowed me to target the investigation to find the problem.
The pic below is from above the "nest" area. We expanded this repair to fix another problem that had plagued him from when they first moved in. That problem was the same...squirrel eaten wires... but finding it was much harder as the entry hole had been covered years before during some painting work.
Part of the "package" if this turns out to be animal caused is to block the entry point to prevent this from happening again.
Wow, they caused some intense damage! So glad you were able to find and fix this for him. I haven't heard any critters, so I'll hope for a short. Thanks so much for the direction!
Troubleshooting and repairing a short in the circuit is the hardest and most expensive electrical work for a homeowner. I've seen many wires in that same condition from one rodent or another; it's not just squirrels. Hopefully you can find signs of some sort to get a start on things. Otherwise it's just hit and miss with troubleshooting techniques. You could get lucky and find it in 10 minutes or it could take 10 hours or more if it's well hidden. And then the building repairs start.
Good luck, you'll need it.