landlord and renter here
yeah, prepaying a year is too strange, it would make me think you are hiding assets... upcoming bankruptcy? divorce? being sued? hiding assets is shady in any case and I don't want shady tenants.
part of the reason it's strange is because most people who have the $ where they could pay in advance are smart enough about money that they'd rather invest it, or they'd rather keep the leverage over me in case anything was wrong with the rental. like, what if *I* skip town or go in to foreclosure or something?
The renter ought to be extra concerned that "landlord who I just prepaid for the whole year" is MUCH MORE likely to disappear than "landlord who needs to maintain this place every month or i'll stop paying".
as a renter, I would prepay like, 2 or 3 months, if there was some doubt about my ability to pay and doing so helped me get approved. but i wouldn't offer that unless I sensed some hesitation, and i wouldn't expect a discount.