An administrator sets the maximum number of messages (up to a limit of 500) that can be in each person's Inbox. If you request more messages, you only receive enough to bring the total number of messages (including follow-ups) to that number.
An exception to this rule occurs to keep cases together. If there are incoming messages from the same person, they will be downloaded together, even if the maximum messages allowed is exceeded. However, two server preference options must be checked: Automatically Refill Inboxes and Exceed Maximum Inbox Size To Keep Cases Intact.