Your answers leave me even more puzzled as there is nothing that is an obvious deal breaker.
When they aren't being scanned I presume that the emails are getting through OK or is email blocked ?
Because of your concern about not having your email scanned you could take some proactive action.
How many email accounts do you have ?
If only one You could try the free version of MailWasher (I use the Pro paid version for multiple email acounts), it is primarily an anti-spam program and it downloads a very small part of your email for analysis and filtering of spam. It displays this small part in text mode and doesn't download any attachments, so it if fairly safe (I exclude mailwasher.exe from avast email scans).
Any email that you think it suspicious, you just flag it for deletion, once you have done that and click process mail, it deletes the email from the email server and calls your email program and you only download what is left, your genuine emails. I love this program as I too am a dial-up user so I don't have to download 'all' email to filter spam or suspect emails. This also means avast only has to scan the remainder (assuming we get it to work).
Something that might help,though I'm not entirely sure as if it isn't scanning effectively it wouldn't be loging, but won't hurt.
It might prove useful to create (for a while) a more detailed avast! log of your mail connections.
You can get the mailscanner to log your connections by editing the avast4.ini file (in Program Files\Alwil Software\Avast4\DATA folder).
In the section headed:
[MailScanner]
add the line:
Log=20
and save the updated file.
Then read in some mail to generate the logging information.
The log will be in Program Files\Alwil Software\Avast4\DATA\log\ashmaisv.log
Before posting the log you should mask any personally identifiable information.