We have a ThermX heater and find that it comes in handy. Unless there's something wrong with it, it's as safe as any unvented catalytic heater.
The advantage is that, unlike the forced-air furnace, it requires no electricity to operate. The disadvantage is that being unvented, you need to leave a window or door open a little for ventilation and you would not want to leave it running while you sleep. (As a general rule you should also have a working LP gas detector and carbon monoxide detector.)
Regarding the pilot light not staying lit, we have a different model with slightly different controls, but we have found that when lighting, you have to manually hold the gas valve open longer than the instructions say in order for the pilot light to stay lit. As I recall the instructions say 30 seconds, but it's more like a minute or two before the thermocouple will hold the gas valve open. If that doesn't do it you may need a new thermocouple.