Hello,
Long press the account in AquaMail, choose Options and Folders.
- Under Account options, be sure to uncheck "Remove deleted messages" (this means "remove from AquaMail messages that were downloaded before, and then found missing, presumably deleted, on the server").
- Under POP3 options, be sure to uncheck "purge when server empty" (this means "purge all locally stored messages when the server is found to have none left")