In Rogue One, we see that particularly large file transmissions are affected by a planetary shield:
K-2SO: We could transmit the plans to the rebel fleet. We’d have to get a
signal out to tell them it’s coming.
It’s the size of the data files. That’s the problem. They’ll never get
through. Someone has to take that shield gate down.
The novelization elaborates, making it clear that the issue is data loss due to interference from the shield (so transmissions are not totally blocked). Whether this is simply due to more opportunities for data loss in larger files, or something to do with the frequency or some such of high data-rate transmission is uncertain, but probably the former:
“We’re fine,” Cassian snapped. For a moment Bodhi heard only long,
ragged breaths. Then Cassian seemed to steady. “We’re changing
tactics. We’re not sure—we may not make it back for extraction, but we
can try to transmit the schematics from the comm tower.”
Bodhi wanted to argue—what exactly did we may not make it back mean?
But Cassian kept talking. “That’s a lot of information,” Cassian said,
“and even the tower won’t be able to push it through the shield
without data loss. Tell me I’m right about this, Bodhi!”
Bodhi forced himself to concentrate. Audio was one thing, but sending
a data cartridge through the shield would be like trying to broadcast
it across the galaxy. Too much data, too much interference. “You’re
right,” he said. “You’re right.”
Rogue One: A Star Wars Story
Clearly such signals are not blocked altogether (probably because they’re low-energy), but they are affected.
It’s not clear how much of this applies to Star Destroyer deflector shields, but it certainly seems likely that similar effects might be in play, albeit at a smaller scale.