Q:

What is wrong with the rabbit living under my shed?

So there is this rabbit that lives under my shed, and I've been watching it through my window for the past few days. It comes out in the mornings, and sits next to its hole crouched in a tight ball, and stays there until you approach. It lets you get within like 4 feet before it moves.  I have never seen it eat or move more than about 2 feet from the shed. I've left carrots, spinach, apple slices and such out next to its entrance, and those are untouched. Is it ill?  should I try to catch it to take it to a rehab? Should I euthanize it?

A:

The fact that you've never seen it eat doesn't mean it's not eating. That just means it doesn't eat while you're watching. Don't feed it. It's not a pet. It's a wild animal and will take care of itself. 
Stop approaching it. When it knows you're watching it, and especially when you get close to it, you're causing it a lot of stress, because it thinks you're going to try to kill it. 
Normally rabbits will graze near the entrance to their burrow so they can escape to safety if danger threatens. As they feel safer, they will venture further from the burrow entrance. If you are constantly watching it, you may be preventing it from feeding because it doesn't feel safe. 
If you back off and leave the rabbit to its own devices, it may start grazing in your yard, which will allow you to enjoy watching it from a distance.

A:

Rabbits are crepuscular coprophages. That means they're most active at dawn and dusk so they're most likely to be eating their fresh greens when you're probably not looking because it's dark and when you do see them during the day, they'll probably be relaxing and chewing pellets.
The one in the picture looks like it's chewing pellets.  They don't need to move much because they, uh, "produce" the pellets themselves.
I'd guess everything is normal here.  If you're really interested, set up a wildlife cam to try to catch its movements when you're not actively watching.

A:

The rabbit doesn't look like it's going hungry, so it's probably just not interested in what you're giving it.  Rabbits favor grasses and leafy plants, so if you insist on feeding it, try something leafy like cabbage.

