Im sorry to tell you that you should have asked for your LOC prior to your leave of absence, to lessen the hurdles.
If you are looking for a "secured" LOC, the bank will be looking for co-lateral (house, other investments, etc), but offer you the lowest rate (3-5%). Im guessing you may be forced into a "unsecured" loan based on your situation, with a much higher rate (~10% APR).
This is considered as leveraging, and viewed as a risk for the banks.
Good luck with that ... You may need a co-signor ...