It may actually be a feature. To be sure I'd contact your carrier. I'm not an expert but I have been a technology professional for 30 years and my guess would be that your carrier has set it to do that.
The reasoning would be something like, most carriers charge for the data you consume providing hotspots. If Joe Shmoe's plan provides him with 25GB for hotspot each month. The first time Joe sets his phone down and comes back, let's say 10 hours later to find that he doesn't have any more data left on his monthly plan because the hotspot was running in the background. Joe will call the carrier and raise cain. Assuming this happens a lot, and I'm guessing it does. The carrier might decide the best option is to set the hotspot to never run in the background.
Now, that said. You may be able to go in to your settings, and enable it to run in the background,I'm not sure. I've never tried it on an iPhone. Considering my explanation however, you may not want to. Or you might. If you do, and it will let you, go for it. Either way, hopefully this clears the mud a little bit. Remember, this is a guess. It's an educated one but it's a guess just the same. You can call your carrier and ask to be certain, one way or the other.
Cheers and best of luck!
