Me and my girlfriend have been dating for a while, and I was at the point of thinking about asking her to marry me. But recently she spent a night with 2 guy friends at an over night camp thing at work. They did things couples do (sit around a fire, play 1-1 basketball) Now she is hanging around one of the guys after work, she swears nothing is going on and she loves me etc. but she has also been acting distant, avoiding spending time with each other and picks fights with me over pretty much anything.

Should I keep trying or is it time to let go?

If she would rather be with someone else, then its time to let go. Especially if you cannot talk and resolve the problem, instead of arguing.

Answer a question for me, do you love her?
If you don't really love her with all that you have, as talaniman said, let it go.

If you do really love her why and the hell would you give up on her? That isn't love, that's infatuation, you like her, you like her looks, she makes you smile, but if you love her you wouldn't let her walk away. Show her you care, step up, be a man, watch some old romantic movies if you don't know how to woo her off her feet. Hell if you have that much of a problem Google it. Plan a romantic date, just the two of you. Tell her how crazy you are about her, make a cd of her favorite songs, better yet songs that remind you of her. Sweep her off her feet.

Most girls go else where for attention when they're not getting the attention the deserve at home. Making her feel like she's the only girl in the world for you might help her realize the same.
Hope I could help.

It doesn't matter if you love her or not, if she has moved on she has moved on and there is nothing you can do. If she has made that decision then that's it, forget it and move to the next chapter in your life.