I agree with everyone else, if you don't set a more healthy boundary here you will most likely regret it. It is like finding out your wife has become an alcoholic but you agree it is ok for her to continue working in a bar. You will see reference to the no contact rule (NC) in just about every reference regarding affair healing.
H:54 W:46 D:11 D:21 M:12 BD:1/15 In-house Separation 2/15 DB started 7/15, W sees consistency 9/15 Dropping the rope and having her leave 2/16, moves 5/16 Reconciliation 1/17 Obviously still struggling