Sadly I have seen this situation many times and often what complicates and skews the entire picture is what's being hidden by one party from the other.
It's startlingly common for one person to apparently go off sex, fudge the reasons for it and when backed into a corner, admit a lack of sexual attraction or loss of sex drive.
What they sometimes keep hidden is that the reasons for this are not connected with a loss of sex drive overall, or a permanent loss of attraction for their partners. It's because they've met someone else.
It can be puzzling if it appears the person is making all the right noises and - threatened with the end of the relationship or living separately - wants to stay put.
Sometimes this is because the other relationship isn't yet on a secure enough footing to permit living together, or risking the loss of the 'sanctioned' relationship and all the benefits it brings. So it is more beneficial to the person having the affair to 'buy time', keep his assets intact and his partner on the back-burner, while he makes up his mind.
If there are secrets like this, it can be soul-destroying and terribly damaging to mental health for the person who is trying to make the other person love her and fancy her again. Fruitless too because if there's a secret affair involved, none of this is to do with her personally and she therefore has no power to impact on the final outcome.
The wisest approach to this is to take control and at the same time, make one's own enquiries about missing bits of the picture.
Regardless of what might be causing this, the single event that causes change and greater motivation to resolve the situation one way or the other is loss.
The most unwise approach is to wait it out and to try in vain to make the other person fall in love with you again or fancy you. If your partner is experiencing a surfeit of needs being met by two (or sometimes more) people, there is no motivation to choose. Plus, most partners would be unwilling to cede all the choices in this scenario to someone who is treating them badly and unkindly.
I would suggest parting and if he wants to resolve the situation through counselling, let him make the appointments and try to resolve this himself. He is the one whose feelings have supposedly changed and so has the responsibility to seek a remedy. However I would caution that couples counselling is a waste of everyone's time (and your money) if secrets are being held.