I suspect it would take something pretty drastic.
Humans have language built into their DNA. Steven Pinker talks about the "language instinct", and while I might disagree with him on fine points, there's definitely something built into us.
Even profoundly deaf babies will begin to babble at the same age as hearing children - the difference is that without the ability to hear spoken language around them, they soon stop vocal babbling. When they're with adult speakers of sign language, though, they start babbling with their fingers! And of course this then develops into full-fledged sign language as the children mature.
In the case of pidgin languages, or languages that come to be used by people of different language groups when they are forced together by circumstance (like Russian-Japanese pidgin, for example), the pidgin itself will have a small vocabulary and rudimentary grammatical system - but once a second generation is born in this language community, the language gets fleshed out by the children and becomes a creole language.
There's something about people - they always want things to mean something. They may not always categorize concepts or objects the same way, but they will categorize. And once categories are fixed, people will automatically try to assign unknown things to known categories. There's a logic to this. If there were no prototypical concept for "apple," then how would we be able to recognize all the different types of apples, and know to eat them? Think of the vast variation in the concept for "dog."
So take a hypothetical situation where people become telepathic suddenly. Will they stop speaking aloud? If the telepathy is effective enough, this seems possible. Will they stop thinking in terms of auditory and visual signals? That's tougher. If the telepathy simply involves the ability to transmit signals directly from one brain to another, I think it would be very likely that the brain would interpret those signals in terms of auditory or visual signals, because those pathways are already primed and have meaning. I struggle to imagine a way that the telepathy would not make use of preexisting patterns of brain activity, especially if it were to be such an effective means of communication that it would supplant spoken language.
Telepathy also has its drawbacks, because I'm not sure if it would be as widely usable in communication with objects, as with programming computers or auto-open doors or other similar technologies. How would you design a receiver for telepathic signals? Or would you rely on written symbols for such communication? The written word is always the slowest to change, as evidenced by the peculiarities of English spelling. We've got letters in the word "knight" that have been around for hundreds of years, long after the sounds they once corresponded to have disappeared.
In language as in technology, there is a tendency for very ancient patterns to persist once they have optimally matured. I would expect that the ancient elements might be difficult for "current" users to distinguish from more recent ones, but I suspect they would still be there, even a thousand or more years into the future.
Thanks to Dave Steffen, known on the forums as steffenwulf/steffenwolf, for suggesting this topic. He blogs at steffenwolf.blogspot.com