This is the problem with communicated deadlines (as opposed to INTERNAL deadlines, that you set for yourself): the wayward spouse will inevitably, one day before the end of the deadline, promise you the moon and the stars for you NOT to give up on them.
Happens all the time.
Affairs are highly addictive, as you have seen. My best advice to you would be to ask your husband to send the OW a no-contact letter, the content of which is to be proofread and approved by you, and it's to be DELIVERED/mailed by you (so that he doesn't add anything or subtract anything). He needs to change his e-mail address, and his cellphone #, with detailed billing on the new #, and the bill coming to you.
COMPLETE TRANSPARENCY.
If it were me, I would also ask for MCing, with a good, pro-marriage MC who specializes in infidelity.
Do you think he would do that?
The recidivism rate on infidelity, even WITH these things, can be significant; WITHOUT them, it's probably 75-90%. Even if he WANTS to end it with her, he's going to be very hard-pressed to do it on his own, and every new contact with her sets back his "withdrawal clock" to 0:00:00. IF he can maintain no-contact, you're looking at several weeks of HARD WITHDRAWAL, followed by up to 6-24 months for complete withdrawal.
Have you done any reading up on affairs? It CAN be done, but it would be best if you knew what you were up against, and decided to ask for the above as your list of "dealbreakers" if he wants to come back.