I assume meltcats do not have a naturally limited lifespan, unlike Earth mammals, and can continuously regenerate their cells. They can also heal a lot of minor and major injuries by melting the affected body part(s) and re-shaping them.

They can only die through diseases, a severe traumatic injury that basically disintegrates them, or entering an invalid body configuration (missing vital organs). I don't know for sure if they maintain their personality and memories if they melt their brain, which if not, could also count as a kind of death.