Sorry to hear about your husband's troubles.
The hard truth is that people make time for the things that are important to them. Sadly, it's likely that your metamour is losing interest in the relationship with your husband. Too busy to communicate even for a moment, once a day? I doubt it. Possible, sure, but still . . .
At the moment, it sounds like he's the only one investing time and energy in this relationship. If I were him, I'd stop chasing her. If she's still interested, she'll contact him. If she doesn't . . . well, there's the answer.
What can you do about it? Depends. If you feel she's not treating your beloved with the level of love and respect he deserves, you can say so. You can certainly be there for him as he walks the path ahead of him, wherever it leads. If it does indeed come to a breakup, you can help him grieve and heal, much like any other personal loss people face in life.
Good luck to all of you, and again, sorry for your troubles.