no, these people deciding on refi work by the book, they have a list and when you have no monthly income for an extended time they will not even look at it, I have seen Schwab handling things different when you have a major securities account with them, but generally all they do is keep the mortgage and do a securities based or supported loan till you have the income again, hardly something most will be able to do. Some insurance companies may bite if you back it with annuities but thats not an easy game either.

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In the past you would have been able to refi, but those types of loans are what has help put America in the pickle(isn't that a nice way to put it) its in now.

I think any ways you should talk to your lender since your credit record is good. you can seek reprieve from them and they should be willing to help you.
they might favorably consider your refinance request or they might even suspend your payment for a limited duration, during which you can find a job.