NEW YORK — Juan Martin del Potro’s stay at the U.S. Open really should be over. Nearly was.

The 2009 champion at Flushing Meadows somehow kept staving off defeat in the fourth round against No. 6-seeded Dominic Thiem on Monday. Del Potro was sick and certainly looked sluggish as can be at the outset, dropping the opening two sets with little resistance. Then he trailed by a big margin in the fourth set, even facing two match points.

Still, del Potro never gave in or gave up, eventually working his way all the way back on the strength of powerful serves and thunderous forehands to edge Thiem 1-6, 2-6, 6-1, 7-6 (1), 6-4 over more than 3½ hours and set up a quarterfinal showdown against Roger Federer.

“Thanks so much for all the support you gave,” del Potro told the boisterous Grandstand crowd that regaled the 24th-seeded Argentine with “Ole!” chants. “It helped me a lot. ... I won’t forget this match.”

It was by far the day’s most enthralling match, with spectators’ roars heard all the way across the grounds at Arthur Ashe Stadium, where Federer was beating No. 33 Philipp Kohlschreiber 6-4, 6-2, 7-5.

The only bit of intrigue came after the second set, when Federer left to take a medical timeout. He said afterward with a laugh that it was so he could get “a bit of a rub on my back — or my bottom — and I didn’t want to do it on court.”

His back had been bothering Federer before the U.S. Open and restricted his practice time, something he blamed for problems in the first two rounds.