Why Would A Dog Suddenly Have A Droopy Tail?

Droopy tail in dogs can be due to

1. Anal gland disease, because infected or impacted anal glands cause pain and this can lead to droopy tail in dogs.
   
2. Traumatic injuries
3. Fractures
4. Cold water tail due to swimming or exposure to cold water
5. Cuts, bites or wound
   
6. Abscess on tail

You should examine tail carefully and get vet assistance for treatment.