It's important to notice in this account that Capt. Fox onboard SS Baltic is not prevented from resupplying Fort Sumter by Confederate artillery, but rather by the rough weather and the lack of tug boats.
Still, he intended to try again, the night of the 13th, but by then Maj. Anderson had already surrendered.
The plan Fox hoped to execute originated with Capt. Doubleday, in Anderson's command at Fort Sumter, but Anderson himself had never supported it.
My guess is that Anderson wanted to surrender before Fox's plan had any chance of success, which would thus keep Anderson & his men cooped up in Sumter indefinitely.
Sure, Catton makes much of the damage done to Fort Sumter, but the fact is, more than two years later the Union navy did vastly more damage without ever forcing Confederate defenders to surrender.
Maj. Anderson was another... ah... "complicated" figure and did not excel in command during the Civil War.
Fort Sumter after the Union bombardment in September 1863: