LLMs are very good at imitating moderate-length patterns. It can usually keep an apparently sensible conversation going with itself for at least a couple thousand words before it goes completely off the rails, although you never know exactly when it will go off the rails; it's very unlikely to be after the first sentence, far more likely to be after the twenty-first, and will never get past the 50th. If you inject novel input in periodically (such as reminding and clarifying prompts), you can keep the plate spinning longer.
So some tricks work right now to extend the amount of time the thing can go before falling into the inevitable entropy that comes from talking to itself too long, and I don't think that we should assume that there won't ever be a way to keep the plate spinning forever. We may be able to do it practically (making it very unusual for them to fall apart), or somebody may come up with a way to make them provably resilient.
I don't know if the current market leaders have any insight into how to do this, however. But I'm also sure that an LLM reaching for a calculator and injecting the correct answer into the context keeps that context useful for longer than if it hadn't.