After Port Gibson, Grant was on the Mississippi side of the river with an army of about 28,000 men. His supply line was a road on the other side of the river about 40 miles long. Supplies would then be ferried across the river at Bruinsburg and carried an additional 10 miles to Port Gibson. Total length of supply line: 50 miles.
Pemberton sent about 10,000 reinforcements to Bowen, who had withdrawn across Bayou Pierre. Total army size 18,000 troops, total supply line length was about 25 miles.
Grant of course turned Bowen with a rapid march on Grindstone Ford, rendering Bowen's position untenable and forcing the army to withdraw across the Big Black. But even before Grant crossed Bayou Pierre, Pemberton sent a message to his commanders telling them that if they do not have the numbers to effectively crush Grant that they were to withdraw across the Big Black because it would be too difficult to supply them.
Why was Pemberton unable to support an army in the field 25 miles away? Lack of wagons? Lack of forage? Lack of imagination? Lack of backbone?
This is the battle that Pemberton presence was definitely needed. Of course, that's easier to see in hindsight.
Initially —and I stress initially— the key here is not so much about the Big Black but about Bayou Pierre. Pemberton knew that regardless of the outcome of Port Gibson, Grant had to be held below Bayou Pierre.
Earlier in April, before Grant crossed at Bruinsburg, Bowen had been ordered to survey the area south of Grand Gulf. Why Bowen did not examine the line of Bayou Pierre thoroughly enough to be aware of its potential crossings is beyond me. He appears to have been completely ignorant of Grindstone, and probably should have at least constructed (or at least asked for) slight works to be constructed at these crossings. But if nothing else, to at least have been aware of them.
As well, Pemberton had previously ordered Lockett to construct Tete-de-ponts at several locations along the south and east bank of Big Black — including one at Hankinson' Ferry. This would have better enabled troops to operate against Grant along the Bayou Pierre in the event of a crossing of the Mississippi below Grand Gulf. But Grant's quick actions prevented the Confederates from constructing the one at Hankinson's (only the one at the RR Bridge was completed— and only partially so.)
Further, there was only one bridge across Big Black in the area located at Hankinson — a single, narrow pontoon bridge. Moving both troops and supplies across such a narrow bridge created huge bottlenecks, making it inefficient to move and supply troops south of Big Black in a time of emergency. Also, the presence of Union naval vessels on the Mississippi made this bridge vulnerable, as one of the vessels could easily push up the Big Black and destroy it, trapping whatever troops there were on the South side.
Without these things it made Pemberton's ability to supply troops across the Big Black for more than 3 or 4 days difficult and dangerous. Besides, the city of Vicksburg and keeping the RR open was the center of gravity in Pemberton's mind anyway. Supplying troops too risky, especially without an already fortified line along the Bayou Pierre.
Additionally, not long after the battle of Port Gibson, the telegraph line was destroyed, cutting timely communications off between Bowen and Pemberton. Before the telegraph break, Pemberton had stressed that Bowen hold the line of the Bayou Pierre, promising reinforcements.
This was only Bowen's second battle as an overall commander. As we know, Bowen's capability as a tactical fighter was superior — especially when he was within arms length of the enemy. But when he was not in the direct presence of the enemy, as he was while briefly holding the Bayou Pierre after the fight, his confidence tended to wane and his imagination to grow wild (or it seems to me).
With the loss of direct communication with Pemberton or Vicksburg, he became wholly isolated. He then began to vastly overestimated Grant's army across the Bayou and perhaps panicked, forcing him to overthink things and to completely neglect potential crossings of Bayou Pierre on his left flank.
Bowen's inexperience made holding the Bayou Pierre impossible.
It didn't help that it was Loring who showed up with limited reinforcements on the night of (I think) May 2. It was Loring who informed Bowen that he had left his flank at Grindstone Ford completely open. This must have come as a blow to Bowen's already shaken confidence. With Bowen undoubtedly inflating Grant's numbers to Loring, the deal was done. It seems clear that Loring did not have the will to try and hold Grant south of the Bayou Pierre, especially against inflated numbers provided by Bowen.
(We also know with reasonable certainty that Loring despised Pemberton. It is my belief that Loring began to poison Bowen's mind about Pemberton's legitimacy that night. For it is after the Port Gibson defeat that the rumors that Pemberton was a traitor suddenly became widespread among the troops —a rumor that would grow to a crescendo by the time of the Battle of Big Black. I have a hunch this rumor was allowed to trickle down from Loring's officers and fester among the troops. It probably began that night. But that's just my conjecture.)
Nevertheless, from that point forward, horse-bound messages between Bowen/Loring and Vicksburg from the line of the Bayou Pierre became erratic and often contradictory. Some messages indicated uncertainty as to what to do with Grand Gulf. Other messages indicated their retreat would be toward Rocky Springs, others across Hankinson, some indicating both directions. In reality, the decision to retreat across Big Black was not solely Pemberton's. I don't think Pemberton disagreed with the decision, although he probably wished that they could have retreated via Rocky Springs. But I can't recall for sure.