I thought I saw a post about something similar but couldn't find it. So I had Piper with me and she fell off an overpass and screamed "ah my legs!" went down to where she was and she would never heal up no matter how long I waited.

Luckily I saved just before it happened so I could go back to when she was fine. I did however push her off again to see if it was a one time fluke and again she never healed.

I had this happen with one of the companions so I shot them then used a stimpak, they got up after that.

Ok good to know, I'll try that in the future.

Mine keeps dying

Yep, I had the same thing happen to Macready. He fell off a very tall overpass. I laughed at him and continued on, figuring he'd just spawn next to me somewhere like always. .. eventually he did, but he was sitting down on the ground. I tried to get him to move but he wouldn't.. so I ran away further.. again he spawned near me sitting on the ground. I then fast traveled and he spawned in his ko position once more. Like the OP, I had a save right before I went up on the overpass. So I just reloaded and everything was fine.