Yesterday I gave Harry an apple twig and he chewed all the bark off and left the inside. Today I gave him another and he has eaten half of it, bark and the wood. I have some more but I don't know how often I should give him one. I know he can eat some wood and it won't cause him problems, but how much is too much? 

Edit to add - his treats (veg, pellets, wood) seem to give him more of an appetite for hay. He always jumps in one of his litterboxes after a treat and has a good munch. So I'm not worried that it will stop him eating hay, I just don't want it to give him digestion problems or make it hard for him to pass stool or anything.

Hmmm....I've given my little girl 24/7 access to chew things (apple wood sticks and willow). I don't think you'll give Harry any digestive issues. Rabbit bodies are made to be able to digest woods. I've always thought of wood as a scrubber and a tooth filler. If you are really worried I wouldn't give it to him for another couple of days to see how his poops are. If he seems I don't see an issue with giving him whenever he wants it. Woods are meant to be given to them to wear done their teeth.

Oh! I did want to ask. The tree you're getting the wood from for Harry. Are pesticides used on it? If there are I would look into finding a way to clean it thoroughly or find another source of apple wood since he likes it so much. I'm just worried about Harry getting sick from ingesting pesticides.

Nope, it's pesticide free and not near any roads or anything.

I bought him some willow sticks but he wasn't interested at all, I think it might be the smell of the apple wood that attracted him. Even with my weak human nose it smells lovely but the willow doesn't have any scent. I will have to keep an eye out for other suitable trees. I will 'rest' him for a few days and then give him another stick if his digestion isn't affected. I've been lucky so far, he's tried 9 different veggies and had no upsets from any of them.

I think so long as he's eating everything else normally it should be fine