First, the buttons will only show if there are fewer than 5 messages in the notification -- since it doesn't make sense to delete "12 unread messages" not knowing what they are, and only 5 fit in a notification.
Second, Android may "collapse" a notification, hiding the details of those messages and the buttons too.
This is independent and out of control of AquaMail, happens when a notification is drawn on the screen.
To expand a collapsed notification -- this varies by make / model / version -- try swiping (pulling) down on it, or "pinch zooming out" horizontally (for Android before 5.0, I believe).