Firstly, deletion isn't really a good first option (you have none left), 'first do no harm' don't delete, send virus to the chest and investigate.
In the Home version avast requires an interactive response to a detected virus, the pro version obviously gives a much more flexible option.
I don't know how this is happening as avast doesn't have any connection capability, it can't connect and can't disconnect from the internet. The only thing I can think of is that there is some sort of timeout setting that may disconnect you, where that is I don't know, but there isn't such a beast in avast.
The other issue is which of the providers detected the virus ?
Check the avast Log Viewer, warning section, the location of the virus will give a clue. If it is a URL then web shield stopped it, if it is a hard disk location then the standard shield detected it.