The HTMAS Sukhotai sank after water flooded its power controls on Sunday night.
Authorities said on Monday they had rescued 75 crew but 31 were still missing in rough seas.
"It's been more than 12 hours but we will keep looking," a navy spokesman told the BBC.
Search crews worked through the night to find survivors and the operation was continuing on Monday, the navy said. They also announced an investigation into the cause of the disaster.
"This has almost never happened in our force's history, especially to a ship that is still in active use," spokesman Admiral Pogkrong Monthardpalin told the BBC.
Officials said the ship went down after it took on water, which flooded its hull and short-circuited its power room.
With the power lost, the crew battled to retain control of the ship which listed on to its side before sinking around 23:30 local time Sunday (16:30 GMT).
The ship had been on a patrol just 32km (20 miles) west of Bang Saphan, in the Prachuap Khiri Khan province, when it got caught in the storm on Sunday.
Three naval ships and helicopters were sent to assist, but only the frigate HTMAS Kraburi reached the vessel before it sank.
MP/PR
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