I have an Insta-Flame HE 20 propane fireplace. It's probably 25 years old. No thermostat that I know of. The pilot light is lit no problem. I turn it on and it lights up good, but it always turns off. It could be 5 minutes later or up to 20 minutes later. I have turned it on several times and it always goes out on it's own. Any ideas of what it could be or what I can check to diagnose?
My first guess was something with the pilot or it's safety features, but you mentioned that it stays lit?
So I did a quick Google search and found the manual for your fireplace: Manual Download
If you read on down, you'll see that it has a few potential solutions to check for. Of the options, I doubt that it is the switch control since it does come on, although not stay on. Depends on the age and type of the switch as it could be wearing out or wires came loose, but that's unlikely to be a consistent problem like this.
The second check listed is for low voltage on the thermopile (thermocouple). It's a heat sensor by the pilot that checks to make sure it's lit. The last option is to clean the burner, but that doesn't sound like it'd be a problem that'd make your fireplace shut off every so often.