Luke evidently dropped it. It's in his hand when the trapdoor opens and not in his hand a couple of seconds later when he exits the chute. Since it's not seen again, we can reasonably assume that it got stuck in the chute somehow.
Interestingly the various novelisation sources we have available seem to be in disagreement with what happened to it next; The new (canon) junior novelisation doesn't mention it at all. The (original) junior novel baldly states that he lost it.
Jabba’s dais slid forward across the floor, sealing the trapdoor. Tumbling through the hole, Luke lost the blaster. He landed amidst the skeletal remains of various creatures.
The Star Wars Radio Dramatization has a line of dialogue to explain its absence when the scene changes.
Threepio: [Off] Where is your blaster, Master Luke?
Luke: Lost it on the way down. I don't see it anywhere.
Whereas the Official Novelisation has an entire (now Legends since it doesn't agree with the film) sequence where the guard picks the gun up and it and the guard get eaten by the rancor. This was apparently inspired by the sequence in the earlier version of the script. When the guard's actions were changed from scared but brave to outright cowardice, they evidently forgot to account for the location of the blaster or just plain thought that audiences wouldn't notice/care.
The guard picked up the pistol from the dirt where it had fallen and began firing laser bursts at the hideous monster. This only made the beast angrier. It lumbered toward the guard.
The guard kept firing. Ignoring the laser blasts, the beast grabbed the hysterical guard, popped him into its slavering jaws, and swallowed him in a gulp. The audience above cheered, laughed, and threw coins.
and
24. INT. RANCOR PIT
Luke manages to get to his feet. The guard is yelling for help. The young Jedi looks up to see a crowd gathering around the edge of the pit and a metal gate slams closed above him. A second door in the side of the pit starts to rumble open. The guard panics and starts to scream. Luke calmly looks around for a means to escape. Out of the side passage emerges a giant brown fanged RANCOR. The guard finds his pistol and starts firing at the hideous beast; which only seems to make it more furious, as it comes at the two men.
In a sudden burst of energy, Luke jumps twenty feet straight up and grabs on to the overhead grate. The crowd is at first startled, and then starts booing at Luke, as he makes his way hand over hand to the side wall, where he wedges himself into a corner. As the guard continues to fire at the monster, it picks up the unfortunate man and pops him into its slavering jaws. A few screams, and the guard has been swallowed. The audience's cheers turn to jeers as Luke struggles to maintain his grip. His foot slips and he dangles helplessly over the howling beast.