As someone who currently does tires for a living I must say you guys are pretty accurate so far.
I'll just add one thing; a "rim leak" (what Seth_TJ suggested) is not a problem associated with just one manufacturer. It happens to all of them, particularly with aluminum wheels. Aluminum will corrode exactly where the tire bead seats. Many people will immediately counter with "aluminum doesn't rust".. well, you're correct. It doesn't. But corrosion isn't limited to just rust
Most aluminum wheels come from the factory coated in a kind of clearcoat, similar to what's used to cover the base coat of your car's paint. It gives it that nice glossy look to it. If it is compromised it makes corrosion much easier. Particularly if a careless tire technician decides to use a wheel weight that has no aluma-guard coating on it (some wheels have a small lip to hammer on a wheel weight. If your local tire shop doesn't have a good aluminum weight to fit it, they may very well just slap on an uncoated lead weight intended for steel wheels only. This is bad, as wheel weights often times take off the clear coat when hammered on. And without the aluma-guard this can be big trouble. Aluminum does not get along well with other metals. That's where most of the corrosion comes from. Think of it as the same kind of corrosion you may get on your battery terminals--caused by the transfer of electrons between two metals).
Best thing to do is goto a trusted tire shop local to you and ask for a flat repair. If they can't find a leak in the tire itself it most likely is a bad valve stem or a rim leak. If you have aluminum wheels, ask for it to be buffed and bead-sealed (when you buff the corrosion off, there will be no clearcoat left. The bead-sealer, basically a liquid rubber, can take its place in that area and can at least provide some sort of buffer for the wheel to slow down the now inevitable corrosion).
Aluminum wheels also corrode from the hub. The hub they rest on is typically made of iron or steel, which causes aluminum to corrode as well. I have seen wheels where the corrosion had spread to the front side of the wheel--UNDER the clearcoat. The clear was still there!
Steel wheels typically seal much better for a longer time. But they still can rust, especially if you live in my area where there's a lot of moisture year-round and we put salt on the roads for the winter to melt ice and snow. Once a steel wheel rusts there isn't much you can do but bead-seal the crap out of it and pray. You can try to grind the rust off all you want, but the wheel will remain pitted. Trust me, I've tried.
Other than that extended explanation, everything has already been covered by others (in a much shorter and sweeter way. I tend to blabber on a little too long sometimes).
Just one more thing; tires very rarely leak because of a manufacture defect. And Michelin is a top quality manufacturer (in my book it is THE top, but there will always be disputes about that).