The 25-year-old Scot, who breezed into the second round with a 10-1 victory over Surinder Gill, was poised to go into the Crucible Theatre record books after clearing 15 reds and 15 blacks in the eighth frame.
But with the third maximum in World Championship history just six colours away, Hendry failed to pot a difficult long yellow, having made 120.
Had he gone on to join the exclusive club comprising Cliff Thorburn and Jimmy White, Hendry would have won a pounds 110,000 Rolls Royce Silver Series from his personal sponsors, plus cheques worth pounds 115,400 from the championship sponsors.
Hendry finished the first session 8-1 ahead of Gill, the world No 207, and the three-times world champion took the next two frames on the resumption to reach the last 16.
Joining him was Ronnie O'Sullivan, who may overtake him as the youngest world champion. The 18-year-old Essex player beat the former world champion, Dennis Taylor, 10-6, a victory which means that the 45-year-old Ulsterman drops out of the top 16 in the world provisional rankings.
It took Ronnie O'Sullivan only 28 minutes to establish a 3-0 lead against Taylor, with runs of 81, 55 and 60, but the 1985 world champion, called on his years of experience to make a fight of it. Two half-century breaks reduced his arrears to 3-2 and although O'Sullivan, the UK and British Open title holder, took the sixth, Taylor drew level at 4-4 and again at 5-5. From then on, though, O'Sullivan was in control, dropping only one more frame on his way to victory.
Jimmy White also came to the brink of a maximum 147 break. But the 31-year-old Londoner broke down - after an early break of 107 in the third frame of his match against Billy Snaddon - as he took his score to 112 in the sixth.
Attempting a thin cut into a centre pocket, White grimaced as the last red stayed out. Had he succeeded, the world No 3 would have become the only player to have achieved the feat twice during the championships.
And the miss seemed to prey on White's mind, because Hendry's 24-year-old practice partner staged a revival. The pair resume their 19-frame contest this afternoon, with White 6-3 ahead after Snaddon, the world No 59, won two of the last three frames.Reuse content