I was wondering about a character like Capt. Jack Harkness (Dr Who / Torchwood) or Capt. Scarlet (Gerry Anderson). Those character types that just can not die, but take all the damage anyway. Is this Mythic Recovery (they take the damage, but eventually recover), or Physical Immunity (they're hit with a weapon but it has no real effect)?

The type of character I'm looking to introduce is a long-lived / immortal person who can be harmed but not killed. They take damage as normal, but eventually recover from it. If taken out, they're incapacitated but not killed. Eventually, given enough time, they will recover. Other than this ability, they're a normal person (no other supernatural powers, just skills and mortal stunts). To me, this sounds like Mythic Recovery - but what's the Catch? Is the fact that they take damage Catch enough, seeing as they recover from the damage eventually. I'd see it as a +0 Catch at best as there's no way around it - they always recover. To me, that isn't sounding like a Catch at all.

What do you think, should this character have a specific, hard to discover, secret weakness (a proper +0 Catch)?