How long could a secret like that be kept?
It would be a massive discovery, and I'm sure those involved with the initial discovery would not be keen to see it hidden from the public.
Once the signal is detected and it's known where to look, it could easily be leaked to other facilities that do not report to US Government (some are through international associations from what I understand, but not certain), as I'm sure any scientist would want to see the results validated through another source.
Sure, it
could be leaked, but it's also entirely possible that the very intelligent scientific minds in charge of such a discovery would be equally convinced that it's in the best interests of society to not know this.
One of the bigger recent scientific debates is what we do if we do ever find evidence of intelligent life elsewhere. The results of hastily jumping in and attempting to make contact for example could be the end of humanity. We have absolutely zero idea how a extraterrestrial life form would process thoughts and decisions, and it's entirely possible they wouldn't view us anywhere near friendly.
You very likely don't want the entire world to know there's life out there if it's been deemed that we shouldn't contact it. The people working at NASA are some of the most intelligent people on this earth, so I imagine they wouldn't be the types (for the most part) to jump in to leak something so dangerous just because they want to.
At the very least, I'm hoping they would get out their yellow notepad and make a quick pros and cons list before deciding to reveal to the public if they did find it.