As old timer Americans used to say, "In for a penny, in for a pound." Meaning, you've put this much time and energy into this hen, so follow it up for a while longer.
We should have stressed that once a hen has trouble with prolapse, they will likely have more prolapses. Infection is a big problem as it becomes chronic, as it may be doing in your hen with repeated leaking of yolks into the body cavity. You are right in thinking this is not going to resolve, but we never know for sure. Since she's under care of a vet, and you don't have to take out a loan to pay for it, then I would hang in there for a little longer.
Your hen is at the tipping point. She will continue to get worse with no improvement, in which case it will be obvious that you should hasten the end, or she will begin to improve in the next day and continue to improve. See what she does today and tomorrow. You will know if you should euthanize.
We should have stressed that once a hen has trouble with prolapse, they will likely have more prolapses. Infection is a big problem as it becomes chronic, as it may be doing in your hen with repeated leaking of yolks into the body cavity. You are right in thinking this is not going to resolve, but we never know for sure. Since she's under care of a vet, and you don't have to take out a loan to pay for it, then I would hang in there for a little longer.
Your hen is at the tipping point. She will continue to get worse with no improvement, in which case it will be obvious that you should hasten the end, or she will begin to improve in the next day and continue to improve. See what she does today and tomorrow. You will know if you should euthanize.