They will break down, and they will fail eventually.
It's more likely that you'll see them cracking while you are cleaning them than to have some catastrophic failure. The sealing washers can be replaced.
You can prolly use Buna-N, O rings or flat stock if you want and get along fine.
Buna-N is the most common O ring material around. Pretty much every black o ring you can fond anywhere (outside of specialty applications) will be Buna-N and it's good to 248F as a upper end working temperature.
The O rings they sell at the BORG will be Buna-N.
Buna-N is also known as: Neoprene, EPR, Nitrile, NBR, EPR, EPT, EPDM
Among those, there are some characteristics that differ including tensile strength and thermal tolerance.
http://www.rubber-group.com/Library/characteristics.pdf
At that 248F temperature the Buna-N, O rings are supposed to seal effectively and stand up to use in a sliding shaft or static seal application.
Of course using propane you might cook off your seals and O rings if the heat from the flames or burner can wrap up to the metal - pretty much like the heat that collects in a pot handle can make it much hotter than the pot if it's above the flame or in the hot air column.
If you are concerned, you can always shield your gaskets with a little strip of any metal, even aluminum roofing flashing, or plain old aluminum foil should serve. A little strip under the bottom of the pot projecting out a couple inches beyond the metal of the valve and barb should provide your seals all the cover they need.