It's hard to imagine that "sometimes the condom breaks" is in fact exactly true. Condoms from a reputable condom manufacturer are well tested and awfully strong. Occasionally someone writes in that once a condom broke, and occasionally someone has a problem with one slipping, but condoms don't break on a regular basis. Maybe you are using them wrong, or you need some lubrication, or you're perhaps just worried about them breaking? If so, why don't you ask your girlfriend to also go onto the pill?
You can get a girl pregnant while she's on her period. There are no such things as "safe periods" if you have a problem with condoms breaking, switch brands, get a proper sized condom, or have her get on birth control. That should help.
You need larger condoms. Find them in your local pharmacy. - Blu