There is no history within the program itself, there used to be a Stats Section but that was very limited and has been removed for revision, but no fixed date for its return.
The file that contains the data is the C:\ProgramData\AVAST Software\Avast\report\WebShield.txt, have you got that file ?
If not (or even if you have) check the avastUI > Settings > Components > Web Shield > Customize > Report and ensure that 'Generate report file' is enabled. If it is enabled then at the very least it should show the time it started and stopped for the day - so it should be getting updated, even if for this alone.
The Show Last Popup option only retains the last popup - if you have had another or you have rebooted - you can't go further back.