Is it common practice to keep PHP objects alive by storing them in session variables?

PHP's website has an article that deals specifically with this: Serializing objects - objects in sessions. There's absolutely nothing wrong with serialize objects in your session but as this article suggests:

It is strongly recommended that if an application serializes objects, for use later in the application, that the application include the class definition for that object throughout the application. Not doing so might result in an object being unserialized without a class definition...

It can still be very useful to manage objects with short, time-limited lifespans. Perhaps you want to communicate with two different kinds of database servers -- having objects that know how to build queries for those database servers can be very convenient. You, the programmer, get to interact with them in the same way, but behind the scenes one might use a unix domain socket to talk with a local PostgreSQL and the other might use a TCP connection from a session pool to talk with an Oracle instance.

Object-oriented programming exist to provide encapsulation and abstraction. Both are useful, even if the objects involved are created, live, and die, in .5 seconds.