For several reasons:

• The Union garrison, even if unmolested, would not have been able to last long anyway without resupply. (Attempts to do so were unsuccessful due to Confederate batteries.) Major Anderson remarked to General Beauregard after receiving his ultimatum, "Gentlemen, if you do not batter us to pieces, we shall be starved out in a few days." It was clear from the start that any defense would be no more than a token one.
• Fort Sumter was poorly sited to defend against a coastal bombardment. Most of its guns pointed out to the sea and not against Charleston, which under normal circumstances it would ostensibly be defending.
• Anderson had 40 guns against Beauregard's 47. There was a qualitative difference between them, however. Beauregard's artillery were sited to deliver plunging fire into the fort, sending "hot shot" (oven-heated cannonballs) that set fires and forced the Union troops to lock up their magazines to avoid explosions. In contrast, Anderson's guns were set to fire in a flat trajectory (one would presume for shooting at enemy ships in Charleston harbor) and could not shoot back effectively at the encircling guns.
• In any case, the Confederate artillery fire was very effective. Beauregard had served as an artillery instructor under Anderson at West Point, in fact. (He would later successfully defend Charleston harbor against a Union naval assault taken by Admiral Du Pont through his well-trained artillerymen; other commanders of harbor defense had neglected artillery practice and fallen quickly.) His guns took out all but six of Anderson's cannons quickly.

In short: Fort Sumter was unable to fire back effectively at Confederate artillery, which in contrast was able to aim fire on it in order to silence the Union guns; this was likely for naught, as Anderson's men were low on supply anyway and were soon to be forced out.

Source: Shelby Foote, The Civil War: A Narrative, Volume I: Fort Sumter to Perrysville (Vintage Books, New York, 1986) pp 57-60