In Star Wars - Episode 4: A New Hope, Darth Vader has a homing beacon hidden aboard the Millennium Falcon. It is thanks to this that the Imperials are able to locate the Rebel base on Yavin 4.
Are they away?
They have just made the jump into hyperspace.
You're sure the homing beacon is secure aboard their ship? I'm taking an awful risk, Vader. This had better work.
Is it ever explained what happened to this homing beacon?
How long was it aboard the Falcon and tracking Han and/or the Rebels?
No mention of its discovery is made during the rest of the movie, nor is it referenced during The Empire Strikes Back. In fact, the Imperials seem to have few solid leads as to where the Rebels are hiding at the beginning of Empire.