A question posed to me made me laugh! Do I sleep? Do I *need* to sleep?
The answer: Yes! I'm not a perpetual motion machine who can go on and on and on like the Energizer Bunny! Granted, it takes me longer to tire out than the average human person, but I can tire out. This happens mainly when I'm taking on many supers at once - especially super strength ones, as they can take a beating and keep on going. And since the average super strength dude is stronger than the average super strength woman, it takes more on my part to finally bring them down (as well as some trickery and strategy)
After such a battle, I need rest. I also need to eat. A lot. A body like mine needs a lot of fuel to keep it powered up. My healing power is especially energy intensive. After a good nap, I'm good to go back into battle if necessary. And if the battle was especially vicious, then I need to sleep a few hours, which is sometimes not easy to do if I'm aching all over.
One last thing about my healing power: it's not like Marvel Comics' Wolverine's healing power, in which he heals instantaneously after even serious injuries. My power is a little slower than that, so if I have something like deep wounds or stress fractures in my bones, I feel it! That's why sometimes I have a difficult time going to sleep until my healing power has healed me enough where I can finally drift off to sleep. And believe me, I welcome the trip to Slumberland in such times!
In short, I am not invulnerable, and I do need to sleep just like anyone else.