If I would have signed a reaffirmation form, would I have then been approved?

In New Jersey, the courts and lawyers generally recommend that people do not sign those reaffirmation agreements. At least one Judge will not allow them to be filed, even if the borrower really wants to do it. In general, the potential disadvantages outweigh the potential benefits. IMHO, banks sometimes get resentful if a person does not sign and so in retaliation they play head games with their borrowers and sometimes act in other ways that seem to me to be petty. To answer your question, I think that banks approve or disapprove modification applications based on the bank's best interests and whether or not a person signed a reaffirmation agreement. Banks have obligations to their shareholders to maximize their profits. Also, according to some federal programs like HAMP a bank has to approve you for a modification if you meet the financial criteria. Whether or not you signed a Reaffirmation Agreement is certainly not one of the federal criteria.

There is no reason to know if the lender would refinance a loan. It is their business decision.

Signing a reaffirmation does not mean a modification will be approved; Not signing one generally prevents a modification, because the debt has been discharged, and the bank doesn't want to risk violating the discharge. If you have substantial equity in the home, want to keep it, and can afford the payments, you could file a Chapter 13, which would allow you to catch the arrears up over time - but you would have to resume the regular payments PLUS pay part of the arrears every month. This would prevent foreclosure, and allow you time to get things in order, or even to sell it and get your equity out of it. You might also see if you could get a new loan through a different lender, rather than modifying the existing one (which will be a challenge on the heels of a bankruptcy, and while you're currently in arrears - especially if you don't have a lot of equity). If you have substantial equity, you might be able to sell it before a foreclosure, but would have to move quickly. If you have little or no equity, start looking for a rental. It takes at least 4 months to foreclose, and they can't go after you for any deficiency.

The bank isn't denying you a loan modification because of bankruptcy, they are denying you a modification either because you don't qualify for the HAMP program or because your credit with them is not good. Try to see if a local credit union might be willing to refinance you. Many credit unions are participating in 2nd chance mortgage refinancing programs.

In 2011 Judge's would not allow you to reaffirm a mortgage. In 2013, most Judges still won't allow you to do it.

That is a huge myth. Banks do not deny because of bankruptcy, that is merely an excuse for the bank not to work with you on a loan modification.