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It sounds like your rabbit is stressed. i realize it is sometimes hard to tell with rabbits. GI upset is the most common side effect of stress.
My advice is to simplify the diet, as your vet recommended, for a few weeks. Just feed pellets and hay. No fresh grass for now. A move to a new place is a big adjustment for a bunny sometimes. Give him time to adjust.
Keep him inside. Your outside grass may have chemicals sprayed on it without your knowledge. You may let him out for short periods of time once he is back to normal. If the problem comes right back, you'll know where the problem started.
There are probiotic supplements that I always recommend to bunny owners when a rabbit has problems like this. My favorite is Critical Care by Oxbow. You can order this online or perhaps your vet has it. Follow the directions on the package, and it will help restore proper digestion.
Bunnies digestive systems are delicate and need to be given consistent feeds. Too much fresh food can really throw it off, and the effect can last for a while.
Thanks for the reply.
Just a few more questions: my husband travels a lot especialy after the move - everytime he is at home, the rabbit seems better. Is it just my imagination, or could he stress about being alone when my husband is away?
And what causes the sudden hairloss?
I gave him a very small piece of carrot a few hours ago and he is still fine, can I continue with this?
Is there any "rabbit safe" toys to keep him busy indoors? I cant let him run around around freely inside - we have wooden floors and its too slippery.
The stress may be at the heart of the hairloss. It also may be due to environment (temperature) and season. If there are no bald patches, just lots of hairloss, this is likely normal shedding. You have a young rabbit, so this may be the first true shed you are witnessing. And it may also be nutritional. If you are feeding more than 20% fresh foods, you may be unbalancing the diet. Those fresh veggies (not the leafy greens...just carrots and the like) are good, but not balanced. Minimize these, keeping in mind that the bunnies stomach can only hold so much. If it is filled with carrots, it cannot get enough of what it needs.
Your bunny will adjust to the "slippery floors". It can hop around just fine on them. There are toys which can entertain a bunny inside, just check out any major pet store or shop online. I caution all owners of rabbits that they are never to be allowed to roam freely in any dwelling, as their chewing is destructive and dangerous.
Remember that bunnies' stomachs and GI tracts are different than ours. what they eat or stress over today has lasting effects. They depend on the bacteria in their hind gut to ferment their food and help digestion. So look at the overall picture. Diarrhea tomorrow may be from treats and stress today (for instance).