I can not fully articulate why "demented patient" bothers me---in part because the reaction may be more emotional, and perhaps because I am not facile enough with language to understand how subtle changes in wording impact the emotional response to how we speak. But here is my best effort:
Perhaps it is because when "demented" is used as an adjective or noun, there is a suggestion that dementia has become a fundamental part of someone's personhood or identity. Also, "demented" as a term may carry historic baggage. Historically, "demented" has had a broader and more pejorative meaning than being afflicted with an illness affecting cognitive function.
Of note, most dictionary definitions of "demented" list descriptions such "mad or insane", "deranged", "lunatic" , "irrational", or "crazy, unbalanced or unhinged." as the first defintion. "Afflicted with dementia" only appears as a secondary definition (see Miriam-Webster, dictionary.com, encarta, wordreference). Seeing these definitions, it strikes me that in the past, the word "demented" must have had highly negative connotations---ie, someone with highly undesirable behavioral characteristics, rather than someone afflicted with an illness, deserving of care and compassion.
On the other hand, when this term is used nowadays, the historic negative connotations are rarely intended. For example I have heard health professionals who are exceptionally committed to their patients use this term. They just intend to convey the concept of a patient afflicted with dementia, and would abhor any negative connotation. Maybe the problem is not the language itself, but the negative societal views of dementia---and maybe it would be better to be concerned with countering these negative views rather than worrying about semantics.
Still, if I had my way, I would ask that we abandon the use of language such as "demented patient" and instead say "person with dementia". But I'd love to know what others think.