I think a bitcoin bank can not work.
A bank earns money by collecting money from depositors and offering them interest in return. The bank uses this money as a fractional reserve, and lends more money to creditors and expects interest in return. The interest for the depositors is being paid for by the interest of the creditors.
In a strongly deflationary environment it's not easy for the creditor to pay back the loan, because by the time the credit falls due for payment the money is already worth more. For the creditor to be able to pay a positive interest rate, his business needs an roi > deflation rate. Many businesses will not be able to provide this when the deflation rate becomes high. Then lending out money for a bitcoin bank will hardly be possible which also makes paying interest to depositors hardly possible.
So, in my opinion, there is no incentive to put bitcoins in a bitcoin bank.
If bitcoins had a stable value, this problem would not exist.
alexk