ChatGPT has 4000 tokens. The whole conversation counts, not just what you write, and when you go over that limit the earlier part of the conversation is out of its memory. If you ask:
"how many tokens is this conversation long?"
You get a rough estimate how many tokens you already used up. In my case it said: roughly 500. In reality it was 802, which I checked in the openAI playground (assuming that text-davinci-003 has the same way of counting tokens). So it's not super precise, and may be an underestimate.
Another way is to ask:
"how many words is this conversation long?"
Then you get in my case an "approximately 745 words", so that seems better. The real number of words was 670. The token count will almost certainly be higher if you talk with it in another language, because it tends to break up words into several tokens in other languages.