Are you breaking them when you take your bow out?
I broke a bunch of hairs when I first started out over the course of a few months. I still have a hard time with bow hair getting stuck in bow fastener in my case sometimes. Both my teacher and the luthier I go to said it was normal for beginners.
Just be careful when removing your bow from your case
If, by chance, though, you see bugs in your case, they might be the problem.
I think a few hair breaks in the beginning is fine...and to be expected.
What 2ndfiddle said about bow bugs. (although I have never experienced that)
But I have had a bow hair breaking spree here and there over time. Nothing seemed to really be a big deal. I have all my original bows from when I started.
Vibrato Desperato.... Desperately seeking vibrato
Bow bugs are very tiny (wiki says up to 3mm), but if you have them you'll be able to tell, you'll see their dead shells in your case. Also, my luthier said that bow bugs will typically stay near the frog of the bow and will eat the base of the hairs first in a uniform line.
You won't be bothered by bow bugs if you practice enough, they only like to stay in undisturbed areas. If you are worried though, take a cotton ball and put a few drops of cedar oil and keep that in your case, it is toxic to them and (possibly) nice smelling to you!
Bow bugs are actually carpet mites. They hate sunlight so keep your bow out of the case unless you're taking it somewhere.
I just posted in another thread a couple days ago that I've had three bows over the past 20 years destroyed by bow bugs. After I found this out a few years ago, my bows are never in the case.
As for hairs breaking on my bows, I've only had a couple hairs that were broken and that was only when I took them out of the shipping tube "Fiddlershop" ships them in, otherwise I've never had hairs break from playing and believe me, I play a lot, sometimes 5 or 6 hours a day.