Twenty-nine-year-old Samantha Rebecca Smith was last seen when she entered the Landsker Stores in the Spring Gardens area of the town at around 8 am that day.
She is described as being of slim build, four foot 10 inches tall and has blue eyes and shoulder length blonde hair.
She also has a pierced left nostril and various tattoos on her arms.
At the time of her disappearance she is believed to have been wearing light blue trainers, a grey fleece type jacket and a white top.
One possibility is that she may have gone and slept in the Canaston Woods area and this area was combed in detail by both the police using dogs and the force's helicopter and mountain rescue personnel on Wednesday, but there was no trace of her.
"We are still investing a lot of police time into this missing person inquiry and are still appealing for anyone who knows this lady and anything about her current whereabouts to contact us," Inspector Les Clark told the Observer yesterday (Thursday).
"Inquiries are continuing by uniformed and CID officers to trace this woman, who may be still in the area or indeed maybe elsewhere."
Inspector Clark also thanked members of the public and local organisations for their offers of help in searching the area.
Any person with any information is asked to contact their local police station or Haverfordwest divisional headquarters on 01437 763355.