The bank first and foremost just wants to be paid. You can continue making the payments on the current loan without issue. If the bank choose to call the note due they probably could but I've never seen that happen when payments are made.
From a financing standpoint the longer you're on title & making the payments on the current loan the easier it's going to be to refinance the property.
My mother passed away a little over a year ago and I'm still making payments on the home so I understand completely what you're going through.