What version of Avast 5 do you have, Free, Pro, or IS? Does it happen at boot or randomly throughout the day? Do you notice it around a time an update is applied?
When you see the notification does it list a specific shield that needs fixed?
When it says it is unsecured, open the avast User Interface (UI), left click the avast icon, Summary section and click on the Show Details option. Check what is reported as unsecured and report what is found.
There is no VRDB (Virus Recovery DataBase) in avast 5 what auto updates you get are the scanning engine and virus definitions.