What does the online status on Viber mean? Does it mean that the contact is msging/calling another viber contact, or just that the app is activated in the phone and running in the background? My contacts complain about me not replying to them even when I'm not using the app at all!
It means that the Viber contact's phone is on, and the Viber service is running.  Check your notification-settings in app.  Is it also possible you have notifications turned off for Viber via Android's app settings?  You can check by going in to settings, apps, selecting the Viber app and making sure the checkbox of "show notifications" is selected.