If you have continued making the payments on the property, the bank cannot foreclose on the property just because your father passed away. Banks will sometimes try to call the loan due at the borrower's death under the "due on sale" clause of the mortgage. However, federal law specifically prohibits banks from doing this when the property is transferred due to death. The bank should allow you to assume the loan. If you do not make the payments, the bank can foreclose for lack of payment. The link below is a link to the law which applies.
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In my experience, many banks are willing to work out terms and give you a mortgage, especially if you have a proven history of being able to pay and good credit. I recommend that you call several banks, if the bank who currently has the loan isn't being cooperative.