Are you using POP3 or IMAP with the Hotmail account?
Do you touch these messages in any way, anywhere (e.g. mark them read on the server)?
You also mentioned deleted messages - are they gone from the server at that point?
If it's a POP3 account and you use "move to deleted", not that messages will not be deleted from the server until you've purged the folder (long press the folder, or configure AquaMail to do it automatically in settings -> Mail, other).