It could be something that some breeders call a fader. It's basically a kit with an unexplained medical problem, that continues to deteriorate because of this unexplained problem. This could be an acquired medical issue like parasites or enteritis, or it could be a congenital medical problem. It would be hard to determine what might be going on without any other symptoms besides lethargy. Usually it is the additional symptoms like messy poop, bloated belly, weight loss(bony), etc, that helps point to what the possible issue could be.
Having diagnostics done such as blood tests, xrays, fecal test(for parasites), uninalysis, etc by an experienced rabbit vet, might help determine what is going on. But because kits are so small and fragile, it can be difficult to have some of these test done, and having them done, you may not get a conclusive answer or way to treat the kit.
http://rabbit.org/vet-listings/
Apart from taking to the vet and having tests done, as well as no other identifying symptoms to help pinpoint the problem, the only other thing I can think to try would be to treat for possible parasites. Fenbendazole dewormer is a good one that is generally considered safe for rabbits, even young ones. I would want to dose at 20mg/kg for 10 days(to cover common intestinal parasites and possible e. cuniculi), and I would keep a close eye on the kits eating and weight, as in some instances it can cause lack of appetite, and if this occurs supplemental feeding would be needed.
http://wildpro.twycrosszoo.org/S/00dis/Parasitic/Pinworms_inf_lagomorphs.htm
If the kit has a pot belly and wasting along the back and hindquarters, this can indicate possible coccidiosis, and this would need to be treated with different meds(albon or ponazuril) that you would need to get from a vet. A fecal float test can help in determining if parasites are the problem, though with cocci, if it is the hepatic kind, a blood test would need to be done to rule this out.
http://www.medirabbit.com/EN/GI_diseases/Protozoal_diseases/Cocc_en.htm (contains medical related photos)
One other possibility that I can think of is that you mentioned bottle feeding the kit. It's possible that this could be the root of the problem as well. It could be whatever milk you are using is causing gastric upset for the kit. Or even the possibility that aspiration has occurred(which is a common risk with bottle feeding kits) and the kit is developing pneumonia. If aspiration has happened, then you need to get the kit to a good rabbit vet immediately, and get the kit on the proper antibiotic(a rabbit safe one). Is there a reason that you are bottle feeding the kit? Was it not eating well enough on it's own?
