When I first wrote to the Adorers of the Royal Heart, I was in poor health. I was told that I could not be accepted. My health has improved since then, and I am now healthy. Should I write to them to tell them so, in case this changes their answer to the question of whether or not my health is an impediment?

You can sure try. You might want to include some kind of doctor's letter, especially if it is something that won't re-occur. They may not want to take the chance, and you might have to start over with an order that doesn't know about your recent ill health.

If you are really attracted to this order, then why not? They can onlly say "no" again but they might say "yes", and after all, it is all in God's hands. I will pray for you.

Should I write to them now, or should I wait until I have been healthy for longer?

In my opinion, the suggestion to get a doctor's letter is a very wise one. If the doctor's letter can say that you ae now healthy and that the same condition will not return, or at least is unlikely to occur in the future then I don't think you have to wait. I don't know what was causing your ill health but if it is resolved, it's certainly possible that the community will reconsider their decision.