Wayne and Lynne Bean have retained the 50,000 baht reward for information that leads to their 43-year-old son.
The Beans spent Christmas on Phuket in a fruitless search for Brett, who failed to arrive back in the US as scheduled late last month.
His whereabouts remain a mystery. Security camera images from Phuket's west coast holiday districts of Karon and Patong show a man who could be Brett making ATM withdrawals and shopping.
Because the man in the images is wearing a motorcycle helmet, there has been no conclusive identification that it is Brett Bean.
Back in the US, the Beans are expected to apply to gain information about withdrawals on Phuket made from a US bank account in their son's name.
Security camera footage associated with those withdrawls may clarify whether Mr Bean has chosen to change his lifestyle or whether someone else is milking his account.
Family and friends remain mystified by the Phuket disappearance. Mr Bean paid a year's rent in advance on his Karon bungalow.
Having told his mother to prepare for his arrival, he then failed to catch flights booked to Bangkok, to Hong Kong and to Los Angeles.
Details of the flights and his passport were later found in his bungalow, along with his passport. There were no signs of a disturbance.
Mr Bean's motorcycle had gone, along with his laptop computer and mobile telephone. Calls to the telephone number do not connect and regular emails go unanswered.
Officers at Karon Police Station on Phuket's holiday west coast have told Wayne and Lynne Bean that they will continue to look for Brett, although no crime has been committed.
Mr Bean's passport will be returned to the US Embassy. His visa has expired so he is now an overstay.
In theory, Immigration officers could detain him and demand that he pay a fine. In practice, expats can and have vanished in Thailand for decades.
Police say expat residents on Phuket change their lifestyles and disappear more often than many people think.
What makes this case exceptional is that all of Mr Bean's usual preparations for departing Phuket, as he does each year, were in place.
Flights had been booked, rent had been paid, goodbyes had been said. His parents went to LA airport expecting to meet him. He was due to start work as a skiing instructor in Aspen, Colorado.
Mr Bean led what many would consider a dream life - surfing and relaxing on Phuket for most of the year, then working intensely for a few months in the snow fields to make ends meet on Phuket.
He was considered to be compassionate and trusting. Phuket surfing buddies said he was more reclusive and not seen on the beach at Kata this year as often as in past years.
He frequented restaurants around Karon and was recognised in several Patong bars on the basis of the missing person flyers distributed by police, US embassy wardens and his parents.
Lynne Bean was weary but undaunted when she and Wayne left Phuket. ''I will be back soon,'' she said. ''Better prepared to find my son.''