At the point when a parent is unable to understand what they need to sign, unless a durable power of attorney is already in place, someone must seek guardianship on behalf of the parent. Typically a child or other relative would be the one to seek appointment by the court. Once the guardianship is in place, the guardian can go to the bank to move, open, and close accounts as needed.
I would talk to your bank and take your power of attorney...Once it is on file with them it shouldn't be a problem...at least if I deposit the check in my account it has not been a problem...