Well if it were me in your situation I would run and not look back. But it's not - you need to decide for yourself.
I'm thinking that at only 2 years and she cheats already - wow!
This is a relationship without the added stresses of kids, a mortgage, sickness and the ups and downs of a long term relationship.
Is she sorry she got caught or sorry for what she has done?
Besides the begging what has she done to show that she is prepared to put you and your relationship first?
Organised IC for herself?
Talked about relationship counselling?
Looked for books to read to help rebuild you guys?
Offered you access to all her phone and email records?
Given you a timeline?
Told you everything?
Gone no contact with this guy?
Infidelity really hurts, I'm a forgiving person too - but it is not the forgiving I struggle with. It is trying to learn to live with the reality of my situation. Knowing my husband would deliberately deceive me and be physically intimate with someone else when he was married to me!
Over a year later this is where I struggle and then there is the trust issue.....
Trying to rebuild a relationship after an affair is hard work and it hurts every day!
Only you can decide what is best for you and if you think your girlfriend has it in her to put in the work that will be required.
Hugs - hang in there and take care of you!