I'm pretty sure too Travelling stopped being used because of the Breaking, but I think it wasn't a matter of willingly abandonning Travelling. For example, It would have remained too useful, and quite safe, for short distance jumps during operations against a male channeler (eg: like at the Cleansing or the raid on the Seanchan in Altara in Pod) even if long distance Travelling had truly become dangerous (I tend to think Skimming was even more: what happens if your destination changes while you Skim? Would any gateway open at destination or would you be caught in the Skimming dimension until you die? We don't know that it's possible to change destination, it's encoded in the weave itself.)

IMO, the distortions and disturbances in the Pattern once chain reactions began and it was all the Wheel could do to hold the physical world together either caused the Travelling weave to stop working, or gateways could still open but opened in the wrong location more often than not. Small groups of surviving Aes Sedai could no longer give sophisticated training (and institutional one was gone) and universal recruiting was gone (it's likely an ajah in the breaking simply recuited sparkers they encountered by chance or tested (or accepted) young women they met only if they were old enough and mature enough and with the right kind of personality, and they wouldn't burden them more than be useful (that's an important factor: AS focussed on survival could only take a very limited number of trainees before this became a burden they could not afford). If AS recruited en masse (which they could no longer do) during the Breaking, more AOL Aes Sedai would have made it to the end. Obviously, what happened is that the number of female channelers went from millions to a few thousands in a matter of generations, meaning AS in the Breaking had largely stopped recruiting and training.


Those groupsof survivors had their own goals and focus, and perhaps they stay as groups for very long, before events or conflicts made them split. They would forcibly have priorities and their small numbers would mean they had only few "specialists" among them anyway, and many of those would have been more concerned with action than teaching. They had no expiration date on the Breaking, they had no idea early on that it would go on for generations and generations, and would end up threatening centuries of OP developments.

It would all result in expeditive and narrowly focussed training of the few recruits, and as the years went by, more and more concerned with day to day survival and killing men. If Travelling was no longer practical, it would not be a priority to teach it, until there was no longer anyone left to teach it. The same would have happened to all the more sophisticated channeling. No facilities, no point in teaching bio-engineering or advanced ter'angreal making for the moment... until all those who could teach those had died. The Restorers no longer had the luxury to give medical training (itnwas the same for all: you could spend years training a few apprentices only to see them die suddenly - there were no safe haven anymore)) and women they could have taught were hard to locate, so they taught an heal-all crude weave to every woman they met and that did' not require a special or rare talent... and then all restorers were gone. And so on. It would only be in the late phase when things were calming down and it was more and more obvious the women would win eventually that some groups that no longer made it their day to day priority to hunt the last male channelers would emerge. By that time, it was already too late for groups that would merge into the Yellow or Brown down the line to find much of the last OP knowledge - in fact it might have taken generations before they even realized how much had been lost., they could only stop it there and preserve what still remained.

Travelling is such a useful weave that would make hunting down male channelers easier and safer, and would let Aes Sedai save their own skins or evacuate people during disasters etc. I can only conclude that one way or another, it either no longer worked during the peak disturbances of the Breaking, either had become totally unreliable or else it was just too dangerous to use... or perhaps a combination of all of the above, that made Aes Sedai stop bothering to teach it as for the time it was useless and for the time they had to focus on the useful only. Otherwise, it would obviously have been one of the basic weaves to teach - and one known by all AS that did not require special talent but only a certain level of strength, and obviously as well, it was no longer part of training.