None of us can tell you what they may accept. It would be wise to bring this up early in the process and let the Loan Officer know what they are up against. Some lenders will just decline, others may want more information and request a letter of explanation.
The main concern a lender has is whether they will get paid or not. A history of not paying your housing expense is not going to help, but only the lender can approve or deny you.
Let us know how things turn out.
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Assistant Director of Sales
ACADEMY MORTGAGE CORP
105 Conklin Street
Farmingdale, NY 11735
(516) 606-9648 Cell
(631) 227-3258 Office
(516) 584-7138 Fax