Richard will just be hanging around, forever, and no one will question it. Why wouldn't Ser Richard live forever? It's Ser Richard, after all!
Seriously though, Viserys has mentioned off-hand that he can 'feel' his mythic ranks in the form of how his power has intertwined with the Imperium. I imagine that if you pressed Ser Richard, he'd admit that his relationship with combat has definitely gone strange. But he doesn't bring it up because... well, it's Richard. He isn't going to voluntarily engage in any lengthy discussions about the nature of magic unless it poses a legitimate danger or is otherwise important.
If growing old started to threaten Richard's ability to perform his duties, he'd bring it up. Since it isn't an issue, it isn't worthy of concern.