I agree about the higher rates like @ChrisTravers mentions, but just to add:
You are asking for more money because it's not a longer contract, meaning you may not necessarily have work afterwards. Yes, it's a "personal issue", but still something to be considered. With longer contracts, you usually can accept charging less because you have some reliability there. If you have a contract for 6 months, you know you'll have 6 months of work and pay ahead for you. With a short term contract, you may not necessarily have that much work available, but you still need to be compensated.
This is not to say you should charge extreme amounts of money, although certain profesionals can; what I'm saying is that you need to be able to live off of the contracts you do have. Most recruiters that I have dealt with already put in a bid for a contract to another party, and are simply finding the lowest-cost way of completing the contract, while they still turn a profit. One company I worked for was notorious for this, and even tried offering me lower then minimum wage for my province on one contract; needless to say, I told them to take a hike after that.
As for explaining to the recruiter: I would mention that you have certain costs that need to be offset with the time. You are basically being paid for your time, and that needs to show it. If your normal rate is $50, and that covers all your expenses with just a couple jobs, then you are free to maybe negotiate a little lower, depending on your other projects. If they are low-balling you for doing your $50/hr work at $20/hr, that is a major slap in the face. Explain that when you do projects, you take the time to ensure the job is done right, and that you are being paid for your time/expertise. Recruiters are trained to get the lowest possible cost for a project, and as long as you aren't desperate, do not go lower then your absolute minimum acceptable rate, in order to keep money flowing INTO your pocket