Soong did not actively keep his work a secret ... at first
In TNG: The Schizoid Man, Dr. Graves is able to recognize Data as Soong's work, and claims that he taught Soong:
GRAVES: No insult intended, Mister Klingon. You see, Doctor, there's nothing wrong with my hearing. My, my, my, my.
DATA: Lieutenant Commander Data
GRAVES: Shhh! Absolutely no aesthetic value whatsoever. Looks like Soong's work.
(Selar is examining Graves behind his back)
DATA: Quite correct, sir! Did you know Doctor Soong?
GRAVES: Know him?! I taught him everything he knows. You could say that I was the father of his work. Which kind of makes me your grandfather, doesn't it sonny?
(TNG: The Schizoid Man)
Soong was regarded a brilliant scientist, but his work on positronic brains had a bad reputation
RIKER: Who? You don't mean Doctor Noonien Soong?
DATA: He was called that here, but his memories indicate he travelled here under a different name.
LAFORGE: Doctor Noonien Soong, my friend, happens to have been Earth's foremost robotics scientist.
TASHA: Until he tried to make Asimov's dream of a positronic brain come true.
RIKER: A positronic brain. He promised so much. And then when he failed completely, Doctor Soong disappeared. Now we know he went somewhere else to try a second time.
(TNG: Datalore)
This dialogue indicates that he was a respected scientist - but not exactly for the work that produced Data. Depending on how much you believe Lore, this is how badly his reputation has suffered:
LORE: Good old Often Wrong Soong. A joke, brother. Actually, he was a genius by human standards.
DATA: But he had destroyed his own reputation by making what seemed wild promises about his positronic brain design, almost all of which failed.
(TNG: Datalore)
He is not the kind of person who shows off his successes
After the attack on Omicron Theta, Soong fled to Terlina Three. He created an even advanced Android version, Julianna, and decided to keep her existence a secret, effectively sending her out to the world without anyone knowing she was an Android (This is explained in TNG: Inheritance)
It's also implied that Soong chose to continue living on Terlina Three, while keeping track on what was going on in Cybernetics:
SOONG: Oh, well. All right, that's enough. Sit down. (he inspects a plant) Beautiful, beautiful. You know, I've been able to keep track of you from time to time. You've become something of a celebrity in cybernetic circles. Data, why Starfleet?
Overall, it seems that Soong was respected, but not for the work which makes him famous. He got famous for promises he could not keep, and ever since, he is withdrawn and doesn't readily share his successes.
Based on all this, I would think that Arik Soong's work wasn't really "usable". It needed Soong's breakthrough, which he had while he was already under cover and didn't share with others.
