My first thought was - you stop praying when the prayer is fulfilled…
But that doesn’t quite work because the fulfillment of a prayer (i.e. its response) can be “yes”, “no”, or “not yet”…
If the response is positive, you know because it satisfies the petition somehow… like say, your daughter was pregnant, and you wanted her to have a safe delivery… well, once it occurs, then there’s no need to pray for a safe delivery because she’s no longer pregnant, so you’d go on to pray for them to live happily…
If the prayer is “not yet”, then it still seems like it could go either way… I think this is more to the point of the question…
I once prayed for one lady who was going through a really nasty divorce, and she was turning to the church in turn… I prayed for her for 2 to 3 years straight… and she did become Catholic, and she was somewhat interested in me as an eligible bachelor, although I could also tell she wasn’t really in any proper mindset to make a love decision… I really felt bad for her though, and I did like her, so my resolve was to simply hold out hope for what was really best for her either way… This was a sort of “not yet” situation…
Well, after awhile I could just sort of tell the prayerful answer was going from “not yet” to “no”… But it wasn’t a hard break sort of “no”… I did everything I could to try to help her out, and I really cared about her, as she did me… and we never did anything wrong… But it was definitely a no… and, oddly enough, while it was a “no” - it didnt really hurt or feel like I was glad to get rid of her - it was just sort of a satisfactory feeling that the answer was no, even though we did the best we could…
So I would look at your petition, the response and how things are unfolding… somewhere in there… you’ll find something that either satisfies the petition, or serves the well being of everyone involved… and that will probably help you to discern how to move things along in the proper spirit…