Personally, it wouldn't matter if it was once or a hundred times, because that once for me is the only time that it would take to finish it. Once the trust has gone, there is nothing left. Just my opinion though. I have a friend who was sent a letter claiming her DH was having an affair with a co-worker. This happened over a year ago. She confronted him, all he would admit to was a snog at the works Christmas party. She believed him, forgave him and thought she could move on. A year later it's eating her up, because she knows it was more, but he's refusing to disclose, and she's scared to dig deeper. So her marriage is a sham.
You're in a better position than her because your DH has admitted to having sex. You now have to think carefully about whether you can forgive and move on. But he really does need to live up to his promise to do 'whatever it takes'. You need all the gaps filled, all your questions answered, total honesty. He did this, it's not your fault. The onus is on him to regain your trust. Take your time.
Many marriages survive an affair, but it is a long difficult process. Counselling might help too.
My friend's marriage will probably fail, because she's too scared to push for the answers she doesn't want to face, and he thinks he got away with telling her the minimum. The cracks are appearing and it's sad to witness.
Totally honesty on your DH's part is the first step for you. Then refection and soul searching on your part to decide if you can rebuild the trust. If you decide to walk, that's your right, and the price he pays for cheating, regardless of how many times.
Good luck.