I guess we're assuming your "contract" is a yearly lease? If you're month-to-month or something, then absolutely you can try to renegotiate.
But the fact of the matter is that the price of an apartment has as much to do with market conditions as it does with the condition of the market, and if, say, midwinter is a difficult time to get the apartment rented, or the bottom has dropped out of the rental market since you signed your lease, the landlord may well be willing to take a lower rent just to get someone in the building.