A contract is exactly the point. Libertarians are all about making and enforcing contracts. If you contract with a bank to hold your money for you payable on demand, it should be available for you on demand. If you agree to leave it with them for a some period of time so they can lend it out at interest, no problem.
If you want to agree to an account where your deposits are payable on demand, but the bank says it might not be there, because they might lend it out--and you're willing to take that risk--no problem (and no one to complain to when you can't get your money). It's all about the contract.
Today, the Fed decides what those terms are going to be, and people just have to accept that the terms are ok. Fact is, they aren't ok.
Fractional reserve banking creates money that doesn't exist. If the whole banking system involved $100 that you deposited, then I borrowed $90 to pay you for some work, then you deposited that $90--you'd have $190 in the bank. If I default on my loan, how can you get your $190 out of the bank?
Multiply this situation by the money in our economy and it's obvious that the Fed and their attempts to manipulate the money supply have (at the very least) enabled our current banking crisis to happen.
I don't believe fractional-reserve banking should be outlawed, I simply don't believe that it should be the government-mandated way to do banking. Whatever agreement you make with your banker is ok with me.