This is a more common occurance nowadays, however there is hope. The first question I wonder about is why you want to refinance. Since you are not getting cash out I assume you want a lower rate or need to get out of an ARM loan.
If you have time to wait then your value should recover in the next year or two as the market recovers in general and you can refinance at that time.
If you are in a rush then you can ask another lender who is not a bank to get an estimate from an appraiser on the value. Some banks are automatically lowering values by 5% to hedge their bets so you may get more value just from going away from the bank.
Your bank might also not do FHA loans which allow higher LTV rate term refinances and they are simply unaware of FHA or are prohibited from referring you to a lender that does them.
There may be other reasons for not approving your loan but those are some good options.
I hope that helps!