Please check your settings for 'Push' as follows:
1 - On
app's level
> Menu button > Settings > Mail, receiving:
Push mail: enabled
2 - On
account level
> long press on account name > Options and folders > Account options:
Push mail: enabled [disabled by default]
3 - On
folder level
> long press on account name > Options and folders > Folders > press the
wheel of the folder where you want to get push notifications (e.g. Inbox): enable/check 'Use Push mail'
Please have a look into the app's FAQ-page:
http://www.aqua-mail.com/?page_id=227> Search for "How do I enable Push mail"
... and last but not least:
• What's your account server / webmail provider?