Yes to your question, but that's not what I was saying.

Here is one of the most popular training datasets : https://pile.eleuther.ai/

If you look at the pdf describing the dataset, you'll find the mean length of these documents to be somewhat short with mean length being less than 20kb (20000 characters) for most documents.

You are asking for a model to retain a memory for the whole duration of a discussion, which can be very long. If I chat for one hour I'll type approximately 8400 words, or around 42KB. Longer than most documents in the training set. If I chat for 20 hours, It'll be longer than almost all the documents in the training set. The model needs to learn how to extract information from a long context and it can't do that well if the documents on which it trained are short.

You are also right that during training the text is cut off. A value I often see is 2k to 8k tokens. This is arbitrary, some models are trained with a cut off of 200k tokens. You can use models on context lengths longer than that what they were trained on (with some caveats) but performance falls of badly.