Does your father actually have dementia? I notice you've posted your question under the dementia heading, but your profile doesn't say so.
There could be any number of reasons for a sudden change in your dog's interactions with your father. Dogs are very sensitive to all kinds of things, such as behaviours they don't trust and smells they fear (that humans can't even perceive), so we can't really guess what might be bothering him/her.
If you'd like to say a little more about what has been happening, perhaps people will have ideas and experiences to share with you.
If your dad has cognitive and behavioral decline maybe he has taken a swipe or two at the dog and now it is wary. Not that your dad would have done this prior to decline but I even notice some poor judgement with my 90 yr old mom towards her little dog that she didn't do 10 years ago. Keep a close eye on both of them when they are together.
I vote for this reason. For years our dog was attached to mom's side. I've notice that mom now swipes at her at times when the dog licks her arm. The dog doesn't like being next to mom anymore. She used to snuggle in close for hours at a time. Now she'll only tolerate it for a minute or two and then move away.
The dog senses something is not right, they have abilities that we humans do not have. If they smell urine or feces they will react and most likely back away, perhaps the dog identifies something odd in the urine/feces.
Dogs are very frightened by instability and unpredictability. It is time actually to keep watch as dogs may actually attack a loved one who is acting in a different or irratic manner, or who "looks familiar" but smells different. They are pack animals and they defend their pack (family) against instability and danger. They live in a world with very little "thinking" and no cerebral cortex to figure things out with; their world is one of sight and smell and especially of the latter. If there is illness (any infections, difference in smell of urine, etc) they may react negatively. Illness is a danger to the pack. In domesticated dogs it is very confusing. Best to keep a good distance until this settles a bit. As a way to read behavior be cognizant of any "yawning" by the dog. Yawning and the ears drooped or back, means they may be uncomfortable. A lurching gait in a human member of the family may also be disturbing to dogs. Remember, the dog is looking for instability, change, weakening that could mean a danger to his pack which is his family. Dogs adapt and adjust readily enough; but for now just take care. Some dogs are more protective and reactive than others.
There could be any number of reasons for a sudden change in your dog's interactions with your father. Dogs are very sensitive to all kinds of things, such as behaviours they don't trust and smells they fear (that humans can't even perceive), so we can't really guess what might be bothering him/her.
If you'd like to say a little more about what has been happening, perhaps people will have ideas and experiences to share with you.