Hmm, I also use ChatGPT as an anti-procrastination tool and task manager, and it's never made a mistake with keeping track of my task list (except that when it sums the estimated times of subgroups of tasks, sometimes those sums are wrong).

Note that it outputs my updated task list every time I add or remove a task (I only asked it to do that one time), so even if old messages go outside of the context window, it's not a big deal because the full updated state of the list is output basically every other message.