On her blog, Objectively Oriented, Maggie Nelson looks at a topic she was debating for a new application - whether or not to use persistent connections to her database.

There's a connection already waiting for you. Yay, right? Well, with MySQL, connecting is actually really really cheap, and frankly, if you are using persistent connections, you might encounter some issues with Apache going zombie on processes that use a connection, effectively taking that connection out of use. Grrr.

She did some research on the topic but found contradicting evidence for both sides. Eventually, what her choice boiled down to was this possible issue mentioned by Jay Pipes (of MySQL):

If you use Apache, Apache can zombie a PHP process and cause the mysql connection to be held until the mysql server restarts...