Are you referring to how fast (or slow) the message is deleted in Aquamail after it is deleted on the server (via WebMail, desktop or some other e-mail client), or it just doesn't happen automatically?
If it is the former, check you sync frequency or enable "IMAP Push" (if supported by your e-mail server).
If it is the latter (which I suspect), - please check if you've accidentally set up your account as POP3 instead of IMAP. (Long press on the account, and then "Options and Folders". If it has "IMAP options", it is an IMAP account, if it is "POP3 options", it is a POP3 account)
If it is set as POP3 account, you have to create a new one (in Aquamail) as IMAP, and delete POP3 account.
If the account is set as "IMAP", then the question is: does the automatic download of new incoming messages work?
Let us know and we'll try to help from there.