Yes, there’s a limit. Right now it’s 4000 tokens (gpt4 has a 32k model but i don’t think it’s available yet, at least with chatgpt). Once you near the limit, chatgpt will start dropping previous messages to stay under the limit. I don’t know what their algorithm is for deciding what to drop. It could be as simple as dropping the oldest stuff. Or maybe taking a long message and replacing it with a summary. But at a certain point, the conversation becomes “lossy”.

As far as I’m aware it will definitely forget things as the history grows. You can “remind” it about things to keep them relevant, and I think a cool product built like OP’s project would take that into consideration for long running tasks.

If it periodically outputs the latest state of the todo list, it won't have the problem of forgetting things from a long time ago.

FWIW that's exactly what it does (updates the current state of the whole todo list each time). After two weeks of use I've never had it make a mistake in keeping track of my total list of tasks. By default (I mean I didn't ask it to do this) it outputs the total estimated time for each category of tasks, and that summation has been wrong (which wasn't that surprising to me, as "LLMs aren't great at math" is a known issue), but even then I just tell it "Can you double check the category totals?" and it fixes them.

They might make it summarize intermittently behind the scenes when the context grows too large. Which would be how it has a gist of the stuff that was mentioned way earlier even thought it doesn't know the specifics.