On the desktop, SmarterMail allows users to see notifications for things like meetings, appointments, task due dates, etc. These are handled via standard "window" notifications. However, many mobile browsers don't support window notifications.
Therefore, while notifications may work in some browsers -- Firefox on Android, for example -- others do not support them. Even Chrome on Android supports it to an extent, but prefers a separate API over what's used in SmarterMail. So, you may see them work sometimes, but not others. As for iOS, Apple always has to be different: iOS doesn't support window notifications at all, in any browser.