GIF needed
Fox's most well known combo has some complexities to it that will be discussed in this article.
For up-throw up-air to be a true combo, you will need to execute an Instant aerial. On a GameCube Controller, this takes some finesse. If you find that your up-airs never seem to hit before your opponent is able to jump or attack, you're probably acting too slow, whether out of the throw or in the air.
Up-air is actually a multi-hit move, making it liable to being dodged with SDI. SDI-ing the second, strong hit won't save an opponent, but they can sometimes SDI the tail hit upwards or to the side such that the strong hit can't quite connect.
Fox does have counterplay. With the right spacing, you can single-hit up-air, leaving the opponent with no way out. There are some easy setups for this; for example, Marth at around 80%, should he make the mistake of full-DI-ing in either direction, can be single-hit by just full hopping at him.
If the opponent SDIs up and not to the side, a sufficiently 'deep' up-air will counter their attempt; they just can't get enough SDI inputs to escape it. At higher percents or against opponents that are sufficiently cracked at horizontal SDI, it may be humanly impossible to hit every up-air, and you may even get reversalled.
Up-throw up-air has a 'percentage sweetspot' on most characters within which it is easiest and most rewarding to land. For some characters, like Jigglypuff, this window expires very quickly, but the reward for hitting it is often taking an entire stock.
Characters like Peach and the Mario Bros. are extremely hard to get any up-throw follow-ups on. On the other hand, fastfallers and Sheik are hard to hit at low percents but become much more combo-able after they've taken some punishment, and Marth is extremely vulnerable to the combo but can sometimes break out with forward-air or SDI.