It is difficult to determine an exact time frame for how long it would take a dog to completely forget about its owner, as it can depend on various factors such as the dog's age, personality, and the length of time the owner has been separated from the dog.
However, it is generally known that dogs have a strong sense of smell and memory, which can help them remember their owners even after long periods of separation. Studies have shown that dogs can remember their owners' scent for up to two years or more, and some dogs have been known to recognize their owners even after being separated for several years.
Additionally, the bond between a dog and its owner can have a significant impact on how quickly the dog may forget about its owner. Dogs who have had a strong bond with their owners are more likely to remember them for longer periods of time, while dogs who have had limited interaction with their owners may forget about them more quickly.
Overall, it is unlikely that a dog would completely forget about its owner, especially if the owner had a significant impact on the dog's life and wellbeing. Nonetheless, it is important for owners to maintain a strong bond with their dogs and provide them with regular love and attention to ensure a lasting relationship.