Take some time and really think about what you want. I had about a month of going back and forth before deciding I would try with no guarantee of staying.
If you do decide to stay then you need to get a transparency plan in place to deal with OW issue. Are you friendly with anyone in H's office who can confirm OW no longer works there? That was great for me, having a close friend who works for BF so I know I can call/email her anytime to check up on him (she has known the sitch from the beginning). And BF knows that I can and will ask people to verify his whereabouts if I need to.
Not feeling a connection is normal. When we started piecing I didn't feel anything for BF. It was comfortable like it would be with anyone you've known for a long time, but that's it. If you work on yourself and H works on himself you can get that connection back.
But it's ok if you decide you've had enough. H is a repeat offender and I know that would make me a lot less likely to want to try.
Again, take the time to sort through your feelings and figure out what YOU and you alone want. I know it's not easy but it's necessary.
If you love somebody, set them free. http://tinyurl.com/2empx2g