I think you're misunderstanding Searle's Chinese Room. It has a response for every sequence of conversation, ever. It doesn't store every conversation that has happened; it stores every possible conversation that's possible, whether it'll ever happen or not.

It would be able to handle the following exchange:

Person: "Here's a cool question, ready?" Room: "Ready." Person: "What was the last message I sent to you?"

It can respond appropriately to the following sentence:

Person: "Hey, I'm gonna say something. Here is a sentence. Can you repeat the previous sentence back to me?"

Otherwise, why bother with all of this AI stuff? Just build Searle's Chinese Room as an index and you have a perfect chatbot.