I've never read anything that suggested Albert Victor inherited his mother's deafness. Besides didn't she go deaf after an illness?
From what I (a complete layperson - my interest in Alexandra's deafness came from having had a Deaf mother) have read, the diagnosis is considered fairly solid and is widely accepted in medical circles. Descendants of her sisters have been definitively diagnosed, and her symptoms (and those of her mother were textbook. Even the onset was textbook - she developed it after a difficult pregnancy, which is extremely common (it's even known as "pregnancy deafness" in some areas of the Deaf community).
Hereditary otosclerosis is not
caused by an illness - if you don't carry the genetic mutation, you won't get it - but it seems that (like type 1 diabetes, celiac disease, etc. etc. etc.) the disease needs to be "triggered" by an environmental factor as well. As I mentioned above, difficult pregnancy is a common trigger, but so is measles.
This is incidentally why clinical otosclerosis pops up fairly irregularly; it's an autosomal dominant disease but most people who carry one of the genes will never develop it because they're never exposed to a trigger. What's more, only ten percent of those who do develop it are affected seriously enough to seek a diagnosis. The incidence is thought to have been greater before the introduction of the measles vaccine.
Sir Henry Ponsonby believed that AV was becoming deaf shortly before his death. How reliable his testimony is I don't know. Reliable biographies of AV (and, sadly, the unreliable ones) repeat Ponsonby's claim.