Yesterday I updated Avast, as it requested, so I guess this is the lastest version - 4.7.942.
Since the update, Windows Security Center always shows a popup telling me I've no Antivirus Installed.
In Event Viewer, I found that each time I reboot I've an error code 1802 that, while I cannot fully translate it, tells something like: "Windows Security Center cannot connect to WMI to execute event queries to find third-party firewall and Antivirus". I found that restarting WMI services, that depend on Windows Security Center - meaning it gets restarted too - solves the problem.
For the record, while my Avast is in English, my Windows XP Pro SP2 box is in Portuguese (pt-pt).