The secret sauce here is the phrase "MySQL server has gone away". This is a specific error that your PHP script is telling you that the MySQL server is no longer available for what ever reason. There is nothing written in PowerPress to make the MySQL server go away. This usually happens for a number of reasons, almost always specific to how MySQL is setup in relation to the web server(s).
Learn more about the MySQL error here: http://dev.mysql.com/doc/refman/5.0/en/gone-away.html
This is not a problem with PHP versions. It could be a problem with how quickly the MySQL server can build the given query though, again that is a MySQL issue.
In my opinion, the fact that it happens randomly implies that your web hosting setup is not consistently providing you enough resources (MySQL) for your web hosting needs. Hopefully this is just a matter of your success exceeding your web server's capabilities, a good problem to have but also means you need a server administrator to manage your web site rather than a low cost hosting account.
One thing you can do is use my Static Feed plugin, which will serve your RSS feeds as static xml files rather than query your database at every request. You need to understand what yo are doing when you use it though, and if you're not familiar with .htaccess files, I strongly encourage you get a server administrator to configure the plugin for you so it is setup correctly.
Otherwise you could use a WordPress caching plugins, but usually they are not configured correctly and they cause more problems than they are worth. Specifically, if they add a comment at the bottom of your pages and feeds (like the WP Super Cache plugin) STAY AWAY FROM THEM, it is a known bug that iTunes will reject podcast feeds that have HTML comments at the very bottom.
