Try putting some absorbent litter in his box, (I use CAREFresh).
Sitting in urine could make him sick, but if there is litter to absorb it he should be okay (but keep putting hay on top of some of the litter too).
I also clean the litter box every 2 days, and wash it once a week to help. =)

It’s okay if he sits in the litterbox… as long as there is some type of absorbent litter in there that is absorbing the urine. It’s not good if he’s sitting on wet newspaper since prolonged exposure to urine can cause urine scald on his legs and butt.

I would go to the pet store and get a plastic cat litterbox and appropriate litter and see how he does with that.

Just keep in mind that lots of cat litter can be dangerous for rabbits. Here’s an article from the House Rabbit Society that explains more…

http://rabbit.org/litterboxes-and-liver-disease-2/

To protect my bun’s feet from touching urine I use these plastic grates that put in the litter box. I have a pet peeve that feet should be clean and not stained, especially if she’s white! I’ve used this method for Chilly, who’s an albino so she’s completely white down to her hocks. I went to Home Depot–lighting department. They sell plastic overhead lighting covers (about 46″x22″x1/2″). It’s the kind that you see in department stores’ ceiling lights. The idea is that urine will pass through the grate never touching her feet!

Here’s what to do: Buy one sheet and use some metal clippers to cut pieces down to the size of your litter pan. The ideal size should fit on the floor your litter pan. Repeat 3-4 times. Stack them up and use a zip tie to secure all of them. Do no zip too tightly because you’ll want to be able to flip the pieces around for cleaning. Place the tied sheets in the litter box for use. Be sure the litter pan has sides high enough so that your bunny won’t pee go over the sides, being that the floor is now raised. I made 2 sets so that I can swap out the clean for the soiled. Having an extra pan is ideal. If your pan is shallow you can try 2 sheets stacked high.

There’s two ways to go about using this method:

Method One: without litter (aka. unfiltered)
Chilly was not a typical rabbit. She didn’t poop while eating timothy hay. Since she separated those tasks, I put the grates in her box without any litter. I changed her box & grates every other day or until I could smell it. I saved so much money for not having to buy litter!

Cleaning was super easy. Take everything to the garbage and remove the grates by the zip tie (so you don’t have touch pee or poop). Dump out everything and shake the grates clean. This may require a bit of banging against the side of the garbage can to loosen any poop stuck in the squares. Next, rise everything. Put grates back in litter pan. Then you’re done! Urine does stain over time, so you’ll want to soak the grates in the little pan with a vinegar-water solution for a few hours every other cleaning or at least once a month.

Method Two: with newspaper &/or hay (aka. filtered)
Posey, my new rabbit poops and eats hay at the same time (typical bunny). I’ve layered the grates in the litter pan: First is a grate, then some newspaper, then a grate, then some timothy hay. By the time I can see the grate below the timothy hay, it’s time to change the pan. Also because there’s a layer of newspaper under everything the squares clog faster and then you’re back to bunny sitting in pee. Cleaning is same as above.

I’ve been doing this for a number of years with great success. I’ve seen some shelters use this type of method as well, so that must mean something’s working. Good luck!

My rabbit is about the same age, Trishh, and he sits in his pan all the time. I use Kaytee clean and cozy bedding and I have a hay dispenser hanging right next to his pan. He sits and uses the pan while eating, and then he just sits there sometimes because he feels like it, and honestly he lays in the pan quite often too. Its a bit gross, but I change the litter out daily to make sure everything is sanitary and bathe him every 2 weeks.
Like everyone else said, as long as there is something to absorb the urine your bun should be just fine (if not a little smelly)

I put a layer of Yesterday’s News cat litter on the bottom of the box, then lots of hay on top of it. The litter does an awesome job of soaking up urine and keeps the smell down. Yesterday’s News is made from recycled and compressed newspaper, and has no dust or chemicals that can harm a bun. It’s also safe for the bun to eat if he actually gets far enough down into the box (which usually doesn’t happen since there’s a lot of hay on top). I also use a high-side corner litter box that I put inside a rectangular plastic storage container, so I can put hay in the litter box and around it. He eats the hay while he’s using the litter box, and I don’t have to worry about him getting foot rot from sitting in urine.

HTH!