Yesterday I encountered this problem. The problem was a kind of global. It could be tracked on https://status.openai.com/.
It started in the morning and continued till the early evening. Sometimes the chat was available but without memorizing the conversation and for little periods of time.
Today the chat works well. I guess the only thing you can do is to wait. I’m not sure, but probably resolving the issue by cleaning the cache and cookies may be a coincidence.