what action can trigger clearing of caches? I have a site that is cached for anonymous users. However it seems that something clears caches every now and then (many times daily.) And it is not result of admins activity. I found about it only by chance, when looking at page_cache table, refreshed it after a while and all records were gone. 
Question: how to start debugging this? What can I do to track what user action or anything causes caches to be cleared? Thank you.
Have you checked whether Cron is configured on your site under Configuration options.

When trying to speed up my site, this article was very useful as Cron will clear cache.

http://www.metaltoad.com/blog/how-drupals-cron-killing-you-your-sleep-simple-cache-warmer