The creature, thought to be a minke whale or a sperm whale, was first sighted four days ago, and was not thought to be in any distress at first.
However, experts have now said that the whale appears to be thinner, and weaker than it was.
Curious members of the public have been warned to stay away from the whale, in order to prevent the whale from becoming alarmed or disoriented.
Experts have added that the whale could be lost, or unwell, which would explain why it is not attempting to leave the Bay area.
Whales are normally found in deeper waters away from the shore, where they feed.
Rescue teams are standing by to help the whale if it becomes stranded, whilst the public have been encouraged to report sightings but avoid causing the animal any distress.