I have been having this same issue for some time now. It is just like you describe it. I can not pin it to a specific time or OS version when I first noticed it, but it is here for sure.
My wife and I have parental devices to administer the kids iPads. We put on screen time limits and noticed that when we take them off or try to delete them they re-appear. They re-appear regardless of where we remove them, parental device or child device. Sometimes (most of the time they pop backup right away) they re-appear instantly and other times it can be a day or two before they make their appearance. I first noticed this about 2-3 OS updates ago and so the last 2-3 updates have not resolved the issue.
All of the devices are fully updated. I have tried turning limits off for a day and then back on and they come right back. I have turned screen time off and back on after a day and the come right back. I even shutdown all but one device, removed all the screen time app limits, powered on one device, and then proceeded to delete or make sure that I removed all of the screen time app limits from the devices. I then brought up the next device and continued like that. A couple of days later the limits were back.
I contacted Apple today and they let me know that someone called them about this and they are actively working on it for a fix. He said it would come in a future update but had no eta for that. For now I shut off app limits. Not great but better than the random app limit time outs.