I have been having loads of problem with tethering as well recently.
I am using an iPhone SE and an iPad Pro 9.7” .
It actually drove me mad for a while until I resorted to doing a network setting reset on the iPhone.
This seems to have somewhat made the connection more consistent, however it is still not as it used to be.
I remember that the iPad would turn the iPhone personal Hotspot on automatically, whereas now I have to do it manually. Also on the iPad, under the WiFi list of found networks I would see a special category called “personal hotspots” with my phone listed underneath it. Now my phone is listed together with all the other networks.
Anyway, after the reset at least now it works reliably (so far).