When will podcasts be automatically deleted in iTunes? I've heard that downloaded podcasts that are visited would be automatically deleted after some time. But I'm not sure about when or which condition does this occur. 

When will the downloaded podcast episodes be automatically deleted if not saved? How to control this event?
You can set this for each podcast subscription. Click on the Gear icon at the top of a podcast list to bring up the Podcast Settings dialog. 

The 'Limit Episodes' choice gives you a number of ways to set how many podcasts are retained, including no limit.