A word for a favor/debt that cannot be repaid

"There is nothing that I can pay you for your deed. What you have done is priceless."

I can't think of anything else, but maybe this will get some ideas started for you.

You can open up the list of possible words by using qualifiers, if you'd prefer.

"I am unable to repay you."

"I cannot reimburse you."

If you're trying to go for a more emotional effect, you might say you are "forever indebted" to the person. I would use this last phrasing, personally, especially in the sample case you've given of saving someone's child.

I would say "What they have done for you is invaluable".

I think there is a more common expression which might express the deep gratitude one feels towards another person, a person who has saved your child's life. I would say to that man or woman

Thank you—I am forever indebted to you.

Typical collocations with indebted are:

• deeply, greatly, much, profoundly
• eternally, forever

Some favors or mitzvahofs cannot be repaid. The act of shoveling dirt into the grave of a loved one is a mitzvahof that cannot be repaid by the person being buried.

Beholden : owing a debt that can never be repaid but emotional vs material