Instagram restricts replies to messages to a period of 7 days after receipt. This is intended to encourage companies to reply to messages promptly.
This means that every time a message is received in an Instagram direct message conversation, the reply window is set to 7 days. As soon as 7 days have passed since the last message was received in the conversation, no more replies can be written. Only when another message is sent in the conversation will you have another 7 days to send replies.