Lifetime of objects in a flask app
Short answer: Depends on when and where the class is initialised.
Objects have little to do with a user logging in and logging out. Object lifetimes are dependent on when and where they are initialised.

Objects initialised outside a function or class are effectively singletons and last as long as the application instance exists
Objects initialised inside a class last as long as the orginal object last.
Objects initialised inside a function exist until the function completes execution.

Now classes that handle database requests are better kept as singletons. This avoids the necessity of creating new database connections every time a query has to be executed. So the easiest way to create a singleton would be to declare it as a variable in a module outside a function or class
I have a web app that retrieves data from a database and displays it on a UI. I have a class called table that handles the database requests based on the URL variables. 
My question is: Does flask recycle objects when a new URL is requested? Or does it keep the objects in memory until the user logs out?
Should I have one table object and just update the query every time the URL changes? Or should I just create a new object?