I'd have thought that fluorine, like oxygen, is a strong oxidizer (fluorine being even stronger), and so fluorides, like oxides (e.g. rust) would be extremely stable, among the most stable compounds possible. Unless I'm forgetting the other side: Maybe the other half of the compound is not a strong enough reducer? It's a hydrocarbon though, it burns well in oxygen...

That said, even oxides do break down when heated. Like, that's what smelting is...

Hm...