According to the official novelisation, it was to save energy.
Moving to the man’s position, the Captain stared into the circular
viewscreen and saw a tiny dot dropping away toward the fiery world
below. “There goes another pod, sir. Instructions?” The officer’s hand
hovered over a computerized energy battery.
Casually, confident in the firepower and total control under his
command, the Captain studied the nearby readouts monitoring the pod.
All of them read blank.
“Hold your fire, Lieutenant Hija. Instruments show no life forms
aboard. The pod’s release mechanism must have short-circuited or
received a false instruction. Don’t waste your power.” He turned away,
to listen with satisfaction to the reports of captured men and
material coming from the rebel ship.
It's worth noting that Vader didn't even consider the possibility that these vital plans would have been entrusted to a mere droid, guessing that the pod simply contained "tapes". Under normal circumstances droids are relatively stupid and lack any sense of autonomy so it must have come as something of a surprise to find that they'd been outsmarted by a toaster:
Vader appeared thoughtful. “It could have been a malfunctioning pod,”
he mused, “that might also have contained the tapes. Tapes are not
life forms. In all probability any native finding them would be
ignorant of their importance and would likely clear them for his own
use. Still …
“Send down a detachment to retrieve them, or to make certain they are
not in the pod,” he finally ordered the Commander and attentive
officer. “Be as subtle as possible; there is no need to attract
attention, even on this miserable outpost world.”
In the new Star Wars story From a Certain Point of View: The Sith of Datawork, we learn that promotions among Imperial gunnery commanders were linked to "kill ratios", and that firing upon a pod registering as empty would count against their score even if they hit it perfectly.
Well, this was interesting. “Are we trying to conserve lasers now?” He
ignored my sarcasm, but his face turned red. “The sensors detected no
life-forms aboard. I thought…um…we wouldn’t have been scored with a
Of course; now his actions made perfect sense. Annoyed with
rebel propaganda that showed Imperials to be poor shots—frankly, the
stormtroopers could do with more targeting drills—fleet bureaucrats
had issued a new policy that tied gunnery officers’ promotions to
their kill ratios. Shots fired at unoccupied escape pods would indeed
be considered wasted. I thought this was a terrible idea at the time.
The new policy would encourage some ambitious gunners to aim for rebel
pilots in disabled vessels rather than dangerous, armed drones. But
the brass never asked for my opinion.
Star Wars: The Sith of Datawork