The second sounds more natural. To sound natural, you need to leave out the word "my" in the sentence. it would sound like this "I was bending over backwards to make up for flaking out on my girlfriend, but it wasn't cutting it". I must add, that the phrase "bending over backwards" means to go out of your way to help and or please someone. Usually the phrase is referencing the act of greatly helping someone with tasks or favors that benefits the person you are helping. It's best used when describing what you did for someone that was in need of help "I bent over backwards for them, but they did not appreciate all that I did". This phrase might not be the best term to use in your sentence to sound natural. It would be best to leave that off and change it to something like "I tried really hard to make it up to my girlfriend for flaking out on her, but it didn't cut it". This sounds more natural because when you mess up and upset someone, you are expressing your sorrow towards that person with acts of kindness and gifts vs. bending over backwards is the act of being extremely helpful to someone who is in need of help, and is usually used to describe helping someone who does not appreciate that help, but not always. I hope this helps.