You should expect it to keep itself up to date as other win7 users are finding, if this were the case there would be many more topics on the forums relating to win7 and updates and I'm not seeing that.
So this issue that you have isn't the norm but an exception, why it is happening on your system I don't know.
A possibly one is if you reinstalled the Pro version trial, once you uninstall it, avast considers the trial completed as you uninstalled it. When you reinstall it, avast's anti-piracy recognises you have had the trial installed before and drops the trial period to 6 days. After that 6 days the Pro trial version won't update.
So you could either register and get a Home licence and enter that into the license key input, that would downgrade to the Home version, but you should be able to update. Or you could purchase the pro license and enter that which would restore the ability to update. Having said that I think at the end of the trial period avast pro doesn't work not just doesn't update; I don't know this for certain as I use the Home version.