Yes, this could be a possibility at any point in time. All you have to do is ask your lender (or a different lender who is willing to refi).
The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author (who is only admitted to practice law in the State of California). For specific advice about your particular situation, consult your own attorney.