Is selling it a rational option in this market?

What is happening is that banks are no longer loaning (creating) that additional money, the reserve requirement is still 10% (just an example, I'm not sure what it is exactly) but that is the minimum requirement, the banks don't have to lend (create) that additional $900 as they don't want to take on additional risk right now (very rational). 3 years ago, the $700 billion in TARP funds would have added trillions to the money supply (inflation), currently, the banks took that money and actually decreased the money supply with it by writing off bad debts or purchasing other beaten down banks at a discount.

It is not a rational business decision.

@Andrew Boettcher as to the cockroaches, you are 100% correct- but it is the same rational, a questionable course of action that is not at all a solution. 

Yes, may hard money and private lenders will not look at your debt to income ration particularly for short term loans like bridge financing and flips.

In regards to debt to income ration , what do banks and mortgage lenders look for and what is most important when presenting financial information?

But you should be aware that people in this tenant's situation aren't always perfectly rational, no matter how hard you try with them.

Don't rationalize (i.e..."

You sound like you're just trying to rationalize the negative cash flow. 

Your instinct tells you to run before it gets worse.You may sit here today and think you will remain rational, but hardly anyone did.