If you're using FastCGI, there's no need for "persistent connections", because if you create a connection it is by default persistent, since FastCGI python isn't request based, but constantly running.
This is how FastCGI works in python, to put it short:
1. Run startup code
2. Run request function
3. Wait for new request, then goto step 2.
In PHP/FastCGI this is different, because only the PHP engine is loaded all the time, while the PHP script itself is executed for each request.
1. Start PHP Engine
2. Run script
3. Wait for new request, then goto step 2.
So the difference is that in Python you can define your own initialization. And that's where you put your MySQL connection. :)