There was a guy who used to sit in front of the laundromat I used and would ask everyone walking in and out for quarters. Each day, I denied him or ignored him till he said one day, "Why you so mean? You never even stop for me." and I told him that if he wanted to get money from people he should probably hide his cigarettes and beer, because I don't give charity to people who are going to use it for their habits.
A little off topic, I know.
Sorry!
I agree with Ards, I think the trust can be regained over time if it was a mistake on the friend's part. But that also depends on the friend, if it's just one in a string of problems or an isolated incident.
My best friend has never really betrayed my trust but did tell a lie to save herself the embarrassment of telling me something difficult. We did discuss it and I told her that being my friend includes telling me things I don't want to hear, and that I might be somewhat indignant about it but it's not going to hurt our friendship. It never happened again after that and we're brutally honest with each other, just the way I like it.