Rabbit losing all of his fur at once!

Hi, I'm new to this forum. I hope someone might have advice to offer on skin conditions. My male rabbit (guessing he is about 9 yrs). started to lose clumps of fur two weeks ago, his third eyelids also started to show. The vet checked for mites and fungus, both negative. She found by lifting his fur you could peel it completely off leaving bald but healthy looking skin, this is happening all over his body and came on suddenly. The vet ran blood work and found a high white blood cell and neutrophil count. His temperature was normal. We started him on antibiotics, probiotics and Oxbow critical care supplement. After two weeks his third eye lids are still showing, (he does have cataracts), but no sign of new hair. I can feel a few small scabs that we didn't notice before under the hair that has yet to fall out around his sides and a couple around his cheeks, not in the tooth root area. His normal diet is Oxbow Timothy hay and Oxbow grain. I had also been giving them small amounts of a pelleted food with the crushed corn and dried fruit just as a treat in the last few months, and hope that I didn't throw something off in his nutrition.

Could stress bring this on? Our household has had changes over the last 6 weeks. We lost two of our pets 4 weeks apart, our 16 year old cat and our 11 year old labradoodle both due to cancer. The day our dog passed away my brother moved in temporarily with his dog (who was born on the streets of Georgia, some kind of hunting dog mix). My brother is a bit loud when playing with his dog, and his dog is of-course curious and excited about the rabbits. The rabbits have an attached large play area with boxes and toys, and a large double story homemade pen.
Any advice would be super helpful. I will try and attach a photo today. Thanks!

I forgot to mention that we had our heat unusually high for a couple weeks while my elderly mother was here for the holiday. We normally keep our house cool which the rabbits love. They definately were not enjoying the higher temperatures between the baseboard heat and wood stove.. Could that sudden change in temps send him into an early weird molt if he just shed out completely by late November?

There is a possibility it might be something very serious. You might want to look into something called sebaceous adenitis caused by a thymoma. It can cause this type of fur loss and scaling of the skin, along with protrusion of the third eyelid because of the mass in the chest compressing major blood vessels. I had an older rabbit with it, and these are some of the symptoms he had, along with an increased respiratory rate and weight loss. This is just a guess of course. It's always possible there could be something else going on instead.
http://www.medirabbit.com/EN/Skin_diseases/Immune/Adenitis.htm
http://www.medirabbit.com/EN/Skin_diseases/Immune/Adenitis_Isa.htm
http://www.medirabbit.com/EN/Cancer/Thym/Thymoma_rab.htm
http://wildpro.twycrosszoo.org/S/00dis/Miscellaneous/Thymoma.htm

Thank you so much for responding and for sharing your story. So sorry for what your rabbit went through. Was there anything that could be done for him? I will take a look at the links and also bring this up to my vet. Thanks again!

I know some have opted to try radiation. I didn't want to go that route. The vet did try steroids in the end, but I think it was too late at that point.

One of the above links shares info on one owner trying radiation for their rabbit with a thymoma. Also, here's some more info on radiation treatment.
http://www.medirabbit.com/EN/Cancer/Thymoma_Guzman_et_al.pdf
http://www.medirabbit.com/EN/Cancer/Thym/thym_irradiation.pdf

Oh no, I am checking out the links you attached and so far they are describing my rabbit. We just lost two pets to cancer. It's so unsettling. Both had large masses in their necks. I buy everything organic or at least all natural. It's so heartbreaking. At least I have something I can have my vet look into now... Thank you again.