How is Thanos even a threat to Earth or the universe, given there exists sorcerer supreme Doctor Strange on Earth which hosts several Infinity Stones right now?
Why can't Doctor Strange make Thanos fall forever?
At the start of Avengers: Infinity War we see Thanos claim the Tesseract from Loki, break it open and get the Space Stone inside which he puts into the Infinity Gauntlet. The Space Stone has the power to let Thanos teleport anywhere in the universe he wants.
Doctor Strange only meets Thanos when he is on Titan and we clearly see Thanos has the Space Stone since he arrives by using it. Even if Strange couldn't work out that Thanos has the Space Stone from this, Banner had already told him.
Bruce Banner: No telling. He has the Power and Space Stones, that already makes him the strongest creature in the whole universe. If he gets his hands, on all six Stones, Tony...
Avengers: Infinity War
Therefore, there would be no point in attempting to make Thanos fall forever because he could simply just teleport himself out of the loop.
Thanos is one of the most powerful being in the Marvel Universe. (I will not be listing his abilities as it is a huge list). But one of his well-known abilities is his Mystical knowledge. This has been mentioned in several instances including : Thanos # 7 (summary here) and Deadpool # 64 (summary here). For instance, Thanos cursed Deadpool with an immortality curse so that he could never die which even Death cannot undo.
For someone being so well-versed with the Mystical arts, I'd say it would be very difficult for Dr. Strange to simply float him away or make him fall forever.
PS: However, unless we fully get to know Thanos' powers in the MCU, we cannot say why Strange can't do what he did to Loki (or as a matter of fact the Time-reversal thingy he did to Dormammu either).