Even as a business owner, you need to take time away from the constant flow of emails. If you’re going on a break, allocate someone to cover urgent matters while you are away. Set up an auto-response and share that person’s details, mentioning that they are able to deal with problems that can’t wait.
Nowadays, some professionals mention in their auto-response that they won’t have time to read through all the emails they have missed when they are back in the office and ask people to get back in touch after a certain date for issues that aren’t urgent.