The furnace is an energy hog. not only does it burn propane to heat the air but it burns Battery power to move the air around.. When the batteries start to run down then the blower can't blow hard enough to sail the sail switch and the furnace quits.
Let the batteries charge a bit and it works.. till you turn it off that is.
NOTE: I am not sure what you mean by "RESET" switch.. the Furnace has only two switches (normally, mine now has 3) One is the thermostat (I will exlain mine) one on the furnace. the one on the furnace is also a circuit breaker and thus a "Reset" switch, but like your 120 volt breakers must be ON for it to work.
Now the T-Stat may have a Reset on it, but that is for the T-Stat not the furnace There may also be a heat/off/cool switch, turning it off, then back on,m will often reset the furnace as well.
Why do I have 3 switches.. Well when I had to re-do my thermostat I got a chea one (The thermostat is itself a switch by the way) so since I used a cheap T-Stat, cheapest I could find.. I put an ON/OFF switch beside it.