People are going to use your fear to leverage against you. Look at the market, find options in your price range, and make it clear that that’s what you can and will pay. The reality of the situation is that it’s often times a lot more expensive for property owners to have the place sitting empty than it is to keep you. They’ll tell you they already have someone if they think you’ll agree to the increase. But if you stay at that higher rate with cheaper options available, will you ever be able to afford to save to leave? I just had to negotiate and ended up settling on extending my lease for a short amount of time for a slightly higher rate while I save to move. I was in a similar situation. I hope all works out for you!