Yes, there is a discount - ask for the monthly rate at the very least. If you plan to be there for 9 months you should be able to get an even greater discount. Note the hotel will probably want the payments up front - weekly or monthly - but that's not different from renting an apartment. They will also take credit cards, and that can be good if you get airline miles on the card you use.
Also negotiate for other things, such as a nicer room, breakfast (if not already free), Internet, health club access (if not already free), and free parking (if the hotel does not have free parking). You can give up daily cleaning service unless that is important to you - go for every other day or maybe even weekly (not less than that). Frequent guest points can be negotiated IF the hotel has a loyalty program. A friend of mine lived in Sheraton for a year and collected frequent guest points the whole time, so don't give it up if you don't have to.
The best thing to negotiate for would be a room with a separate bedroom (a real suite) or at least a room that is like a studio apartment and has some separation between the bed and the living area . The worst thing about living in a regular hotel room is you are living in a bedroom.
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