If Decker can suppress Volkoff/Hartley's intersect programming, and Mary Bartowski can do it for Chuck in season 4, why didn't Shaw's intersect just get suppressed using the blue images?
I don't know how much of Chuck you have seen, so apologies if I give spoilers ahead.
Once Shaw has lost to Chuck (in Episode "Chuck Versus the Ring: Part 2"), he subsequently loses the Governor which regulates both Chucks' and Shaws' intersect, Shaws' intersect now becomes useless.
After Daniel Shaw's capture, Shaw became involved with Decker, by flashing on him. Because of this flash, Shaw knew all of Decker's dirty secrets. Most likely, because he blackmailed Decker, Decker saved Shaw from getting "de-intersected". Along with the fact that since without a Governor, his intersect was essentially already "suppressed".
Later in Shaw's return in "Chuck Versus the Santa Suit" another show down is held between Chuck and Shaw. This time Shaw has a new intersect granted from the "Omen virus" labeled as the "Intersect 3.0". Shaw was going to upload this to his brain until Chuck thwarted his plan once again, by reconfiguring the Omen Virus to erase Shaw's Ring Intersect upon uploading it into his brain, instead replacing it with images of Santa Claus.
Essentially Daniel Shaw has no intersect now.
Source: Chuck Wikia
SPOILERS… sort of.
Okay here's how I see it. They left Shaw captured with his intersect because the government is still interested in the intersect and now they have a live test-prisoner who nobody cares about so they can basically do whatever they want to do. So until he got out, he was a valuable test subject.
Sometimes people ask why his mind didn't deteriorate without the governor. My answer to this is that he would've been in solitary confinement with nothing to flash on, so the deterioration would've been kept to a minimum. (perhaps contradicting the test subject theory but who cares it's a hypothetical.)
Another way to explain is that he was intact suffering from the intersect and it had affected his sanity. He did go from 0 to crazy outrageously fast after he got that sukka the first time.