There is no necessary action to take after you have communicated with a guest, and then sent them a preapproval and they have not responded. It may be that they found another place to stay, or maybe they are still thinking. I have sometimes not heard back, thought the guest found another place, and low and behold 3 weeks later out of the blue I hear from them again and they want to book after all. SO you never know.
Preapprovals expire after 24 hrs, so you don't need to remove it after 24 hrs since it has expired by then anyway.
I dont' archive conversations with guests, because I like to have all the history of all my conversations there in case I need it. Think of it this way: in your dialogue with a guest, you are finding out about them and also perhaps screening them to see if you feel they would be a good fit for you. If you get to a certain point with this, and then archive it all because the guest didn't respond, what happens if they get back in touch with you a few weeks later, or the following year (for a different stay) and you have lost all that dialogue? Now you have to repeat the questions and the whole conversation because you've lost it. That is why I don't archive conversations.
IF the guest hasn't responded, you might drop them a short note asking if they are still interested, and letting them know you would love to have them stay. This encouragement might prompt them to reply to you.