Hi,
Try to reset Accessibility.
To do so, go to your device's phone Settings > General management> Reset> Reset accessibility settings (since each device is different you might have to search for "Reset")
Also, check your phones battery power saving settings to make sure the app does not get killed.
I have a further question to throw into the ring.
Having also done an accessibility reset and re-enabled the Web Shield and also the Malware Uninstaller (Avast). There is also the Malware Uninstaller (Avast) shortcut. This places the little man at the bottom of the screen, navigation bar (which I have never liked) what purpose does it serve ?
I have never been clear about what this actually does and the wording in the app doesn't make it any clearer. e.g.
Why would this so called shortcut need to be on, if you have in effect already given permission for the main Malware Uninstaller (Avast) option ?
What would the impact be if you didn't enable the Malware Uninstaller (Avast) shortcut (e.g. what the hell is it there for) ?
Battery Settings:
As far as More Battery Settings goes, I think the Adaptive Battery option one of the areas that can cause issues, so for some time I have had that disabled.