Diagnosing Quality Loss Past the Trained Context Length

Your team fine-tuned a model that was originally trained with an 8k token context window, and now wants to serve it at a 64k context window because the product needs to summarize long documents. Early testing shows the model handles the first ~8k tokens of a long document fine, but coherence and instruction-following degrade noticeably for content further into the document, well before the 64k limit is reached.

1. Why does this happen even though attention, mechanically, is perfectly well-defined at 64k tokens — nothing crashes, nothing is out of bounds?
2. What is the connection between this failure and the model's positional encoding scheme specifically?
3. Name a mitigation you'd propose, and be explicit about whether it requires retraining or can be applied at serving time.