A couple examples come to mind.
In the example of the Tower of Babel, God was able to make languages unrecognizable immediately. Maybe that is a replicable phenomena. And not explicitly or necessarily by the hand of God. An effect on people's brains during space travel could confound their language.
Another example is the Mayan language. It is still spoken in regions of Mexico, and various dialects are spoken in Guatemala. Sorry I have to dodge the question a little. I can't say whether the ancient Mayans would recognize any forms of modern Mayan. But here's my take on it. Introducing a new language (Spanish) didn't break the Mayan language. And the Guatemalans handled the changes far differently than the Mexicans. But even Mayan has a pretty well theorized etymology tracing back to Proto-Mayan from around 5000 BC. The thing is, I think it's safe to say the origin is unrecognizable because, well, who knows what Proto-Mayan is? Especially if you're talking about the average layperson?
That took a thousand years or so. But I think you are pretty free to pick almost any length of time.
Factors that would speed up the process would include:
- losing records of the language,
- losing the Japanese culture (through blending of cultures. The older generations might hold on for a long time),
- special effects comparable to the Tower of Babel,
- regional differences between colonists (and a region with a new dialect becoming dominant),
- losing the language of origin
- lots of people who love to make up words and disregard old words.
Factors that slow down the process:
- Stable, powerful Japanese culture on Earth,
- Well documented Japanese history and language on Earth,
- But to recognize colonist language, Earthlings have to receive some communication from colonists, which is apparently impossible??
To make my answer slightly less vague, I would say a minimum of more than two generations for colonists to stop recognizing Japanese. It usually takes immigrants more than two generations to fully adopt a new language and lose their old language. It should also take more than two generations for Earthlings to not recognize colonists, assuming colonists change their language immediately. As a maximum, I would say 2000 years for either culture's language to become unrecognizable because I think the laypeople of most languages don't recognize the 2000 year old version of their language; the 2000 year old version was probably not the language but its likely dead parent languages. I think Japanese could become a dead language that laypeople don't recognize in 2000 years maximum, probably much less.
We seem to be able to trace just about any word etymologies back hundreds and sometimes thousands of years. To lose all trace of that, the Earthlings would probably have to lose all trace that the Japanese sent the colonists out in the first place, and they would have to lose all traces of Japanese. Again, you have a lot of freedom with the time frame for that.