Ooh, just noticed this.
As Bonsai Doug mentions, it is a "Phra Pidta". One does not typically see these represented in buchas/statuary, being more typically made as votive tablets or amulets to be portable.
"Phra Pidta" is a more current Thai name. The archaeological evidence indicate that the older Siamese appellation was Bakawambodi. This is believed to be a corruption of "Phra Gavampati", Gavampati being possibly one of the first 11 Arahants (according to the Pali Vinaya), or one of Ven Sariputta's disciples (according to the Mahasanghika Vinaya).
There's supposed to be an 11th century statue of Gavampati attested from Burma's 11th century, dedicated by King Anawrahta.
As to why it has this peculiar iconographic representation, even Ven Dhammanando could not trace its origins. The Pali tradition credits him with having stopped a tsunami in its tracks, but I can't see how that relates to his eyes being closed.