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It would be possible to create a CRON job to run, say, every 15 minutes and do something like

chmod 0755 /path/to/your/site/root

where /path/to/your/site/root should be substituted with the absolute path to your site's root.

However, this "solution" is just dealing with the symptoms, not the problem. I would try to find out what modifies the permissions of the site's root. For starters, I'd look at the Global Configuration of the site and make sure that the temp-directory and logs directory DO NOT point to the site's root. Why? My hunch says that they do and some extension is trying to give 0777 permissions to either of those directories. Since the directory is equal to the site root you get this kind of an issue. If this is the case, I'd also find the extension which forces the 0777 permission and contact its developer immediately. 0777 permissions are a bad idea with very few exceptions.

You're welcome! When I was a Linux newbie I had to resort to posting on my local LUG's mailing list with embarrassingly trivial questions. The people there, most of them system administrators in universities and corporations, were kind enough to reply to me with abundant patience and something meaningful which would allow me to find the solution. I'm trying to do the same as much as I can :)

You're welcome :)