Hi Jaimie,
You need to separate these birds immediately. Your hen is going to die if she keeps laying eggs. Finches aren’t intended to lay eggs over and over like a domesticated chicken. In the wild, they only breed and lay eggs once a year and at most might have 3 clutches. Then they do not lay eggs again until the next year. If your hen is already showing signs of being exhausted, what is really going on is she is running out of resources and the next thing that happens is she will die. Split them up and put the cages in separate rooms if you have to. Keep them apart for a minimum of 6 months. You can discourage him from wanting to nest and her from laying eggs by limiting their light to 8-10 hours by covering the cages early each evening. You can also move the cages around at least once a week, and rearrange things inside of the cage. They only nest when they feel like they have a quite, safe place to nest. Keep them in a room with a lot of activity, limit their light and move them around and this usually stops them from wanting to breed. When you do try them back together in the same cage, if the male continues to chase her, then they simply can’t be in the same cage anymore. It’s better for them to be separate than for her to die from egg laying or because he harasses her too much.
Thank you for asking Lafeber,
Brenda