You configure an Exchange ActiveSync device to keep messages for 30 days. On the initial sync, 30-day-old messages are available. However, the next day, you notice that the oldest items have been removed. The oldest item is now less than 30 days old.
To fix this issue, install Cumulative Update 11 for Exchange Server 2013.
Microsoft has confirmed that this is a problem in the Microsoft products that are listed in the "Applies to" section.