Am I dumb for sticking with a girl that cheated on me?

I've been with my girlfriend for two years, and we have what I believed was a loving, committed relationship. But two weeks ago, while she was in the shower, her phone went off and I went to grab it, discovering a text message from some other guy that seemed suspicious. Needless to say, by looking through her phone, I found out she had cheated on me. We went through several days of not talking, then we met up and she professed how much she loved me and that it was a "lapse in judgment" and a stupid mistake. She said she was stupid for it and let her guard down, and it just happened. And she says it will never happen again. I decided to stay with her, but told her it will be a long time before I can trust her again, since a) she did not tell me about it on her own, but I found out myself and b) she'd been lying to me for a month to cover the thing up. Do you think people like this really can change, or do you believe "once a cheater, always a cheater"? I'd like to believe she really is sorry and will never do it again, but I just don't know.