I assume the OP is asking about the US garrison's surrender on 23 December 1941 and not the Japanese surrender on 7 September 1945.

Well, while the Wake garrison had beaten off the first Japanese assault of 11 December, the second assault on 23 December was a considerably larger affair. The initial landing involved some 300 Japanese troops with a modest degree of naval and air support. Wake's repulsion of this invasion force led to a larger invasion force of 1100 SNLF troops plus considerably more air and naval support. The latter support included two aircraft carriers of the Second Carrier Division. Additionally, the Japanese considerably softened up the island between the two invasions with regular air raids.

So Commander Cunningham's garrison was in dire shape in the aftermath of the first invasion. The Wake defenders were already operating on a shoestring. The beefing up of the island's defenses prior to Pearl Harbor had led to the usual SNAFUs such as bomb racks for the Wildcats that did not fit. There were shortages of all kinds and the amazing thing about the first defense of the island was that it succeeded in spite of these obstacles. But heroism was not going to summon up spare parts and ammunition out of thin air. Added to this, Wake was not an ideal place to hold out on a siege. The atoll had no freshwater sources and the post-11 December bombings damaged some of the garrison's freshwater converters.

So by the morning of 23 December it was clear to Cunningham that the situation was lost. The garrison had lost air superiority and the Japanese had successfully landed on the island. Cunningham consulted with USMC Major James Devereux and the two decided on a surrender. Cunningham knew that there were no friendly forces within 24 hours of Wake and Devereux admitted postwar that there was nothing the Marines could have done to stave off the inevitable.

In hindsight, the Wake garrison did everything within its powers to fight off the Japanese advance. The defense of the island was a somewhat slapdash affair that initially succeeded due to a combination of Marine ingenuity and Japanese carelessness. But the garrison was never going to survive a prolonged and determined Japanese siege. Wake was too far into Japanese-surrounded territory to survive long, even had the USN's relief effort had succeeded.