The danger in using too high a wattage is overheating the fixture, especially if insulation surrounds the fixture. The fixture should have a sticker next to or on the socket with the wattage limit. As to why they're burning out so fast, it could be any of a number of things. One is that the garage door opener is shaking the bulbs so you need to use bulbs made for use on openers.

Even if you don't have a garage door opener, just the manual opening of a garage door could be shaking or vibrating the bulbs enough to keep them from lasting long.
They make special bulbs for garage door openers and ceiling fans.

For an old guy that sold light-bulbs at one time, I think its the way the bulb is made and you can find an bulb at Home Depot that will work in this area that your wanting...

Ceiling Fans also blow lamps !!!

You might want to check to be sure that the circuit is wired correctly. I don't know for sure if this is possible, but if a do-it-yourselfer wired it incorrectly, I wonder if the voltage in the circuit could be too high. That might be why the bulbs fry so quickly. Of course, any thing else on the circuit would also be subject to an early demise. The earlier posts about vibration sound more likely to me, though.

I had a problem at one time with bulbs blowing (not just in the garage).

A person turned me into the direction of 130 volt bulbs, instead of the 120 volt standard.

Home Depot sells them in packs of 12. They are contractor packed in a brown box. Look closely at the label though for the 130 volt rating.

Try those, and if by coincidence, they don't blow after the time your others are, then possibly you are experiencing some voltage spike to those sockets above 120 volts.

Or maybe you have found a solution by now. Good luck.

Robert