The plugins connection pool is created when PHP initializes its modules (MINIT) and free'd when PHP shuts down the modules (MSHUTDOWN). This is the same as for persistent MySQL connections.
Depending on the deployment model, the pool is used for the duration of one or multiple web requests. Network connections are bound to the lifespan of an operating system level process. If the PHP process serves multiple web requests as it is the case for Fast-CGI or threaded web server deployments, then the pooled connections can be reused over multiple connections. Because multiplexing means sharing connections, it can even happen with a threaded deployment that two threads or two distinct web requests are linked to one pooled network connections.
A pooled connection is explicitly closed once the last reference to it is released. An implicit close happens when PHP shuts down its modules.