I think your banker summed it up pretty well. If the bank knows you don't have any alternatives, they probably don't have an incentive to reduce your rate. They would probably argue that you agreed to the current rate, so the first solution shouldn't be for the bank to make less money. With that said, if you are severely under water on the property, you could try to argue that if you don't get some help, you are concerned about being able to make the payment, and the bank would ultimately lost money on the deal. Your most likely scenario would be to extend the loan term to lower the payments, which would result in you actually paying more interest over the life of the loan, but at least it would be a lower payment.
It's admirable that you stuck it out when so many others simply walked away. Unfortunately, when it comes to credit and lending, banks care more about cash flow and collateral when considering a refinance of the debt. If the property is still under water, it will be hard for another lender to help you since a default would likely result in them losing money.