Follow Jake's links for nicely illustrated instructions how to solve the problem.
At one link they recommend using Locktite on the screws, and I agree. However, be aware that there are a number of different Locktite formulations and you need to be careful which version of Locktite you use. Do not use the strong hold, heavy duty type that you have to heat up if you ever need to get it to release (Red 271). Also I would not use Locktite Green 290, which is thinner and designed to wick into already assembled parts... It might intrude farther into the camera than it should.
Use Locktite Blue 242. Remove each screw, one at a time, and place a tiny amount of the Locktite on the threads, then reinstall the screw. I've done this with all the hot shoes on my cameras, off-camera shoe cords and other places where frequent mounting and unmounting can cause screws to loosen over time (i.e., lens bayonet mounts). The Blue 242 type of Locktite is adequate for the job and yet allows easy disassembly later. This stuff is generally recommended for larger screws (1/4" and larger) and not recommended for plastics, but I've used it on smaller screws and plastics without any problems.
You are going to need a miniature cross point or Phillips screwdriver to work on those screws. Best guess, it's probably a #0 or #00 (the markings are worn off the one in my toolbox!). Also shown at those websites, they are using a miniature flat screwdriver to coax the finishing plate off the hot shoe. There are inexpensive sets of miniature screwdrivers that have several sized of those and a couple sizes of cross-points, that might be the easiest solution and may be handy to keep with your camera gear or other purposes, too.
Another thing that you may want to consider... get a flash bracket and off-camera shoe cord. This can really improve your flash work, by moving the flash away from the lens axis. Redeye and shadow problems will be greatly reduced. It also puts a lot less strain on the hotshoe and top of your camera. I'd rather break an off-camera shoe cord flash mount than the hotshoe of a camera. It's far cheaper to replace an off-camera cord, than to repair a camera's hot shoe. There are Canon brand off-camera shoe cords, as well as much less expensive ones from third party manufacturers that work just fine. Canon doesn't make a flash bracket, but there are many good ones, at a wide variety of prices. I use a cheap one I got off eBay and a larger, more adjustable heavy duty Manfrotto bracket that cost a bit more. I've also got a couple specialized flash brackets for use with lenses that have a tripod bracket, that attach to any standard Arca-Swiss type quick release.
