I love her very much ... Is there a way to continue this relationship?

I'm with my girlfriend two years ago, in the first period of our relationship i did things she considered it treason, but for me I was considered a normal mistakes, but I promised that I will not repeat these things again and we get through these problems, and then she always doubting on me, even though I tried to make her sure about my sincerity .. I did not leave a ways to make her believe that I love her with sincerity and without fraud, but the result was always the contrary, and doubts are greater every day more .... I spoke to her with this subject often, but she says she loves me a lot but she lost her confidence on me and she cant continue this relationship, I love her and I can not leave her because I know that in fact there is no problem I love her and she loves me and what happened in the past was a misunderstanding, but I can not persuaded her... Help me, please