I understand that each page refresh, especially in 'AjaxLand', causes my back-end/code-behind class to be called from scratch... This is a problem because my class (which is a member object in System.Web.UI.Page) contains A LOT of data that it sources from a database. So now every page refresh in AjaxLand is causing me to making large backend DB calls, rather than just to reuse a class object from memory. Any fix for this? Is this where session variables come into play? Are session variables the only option I have to retain an object in memory that is linked to a single-user and a single-session instance?
Since you mention Ajax, I think you might want to consider the following points:
Assume this large data set is static and not transient, in the first call to Ajax, your app queries the database, retrieves lots of data and returns to the client (i.e. the browser/JavaScript running on the browser, etc), the client now has all of that in memory already. Subsequently, there's no need to go back to the server for the same data that your client already has in memory. What you need to do is using JavaScript to rebuild the DOM or whatever. All can be done on the client from this point on.
Now assume the data is not static but transient, caching on the server by putting them is the session won't be the solution that you want anyway. Every time your client sends a request to the server, and the server just returns what's in the cache (session), the data is already stale and there's no difference from the data that the client already has in memory.
The point is if the data is static, save round trips to the server once you already have data in memory. If the data is transient, I am afraid there's no cheap solution except re-querying or re-retrieving the data somehow, and send everything back to the client.
If your data is user-specific then Session would be the way to go. Be careful if you have a web farm or web garden. In which case you'll need a Session server or database for your session.
If your data is application-level then Application Data Cache could be the way to go. Be careful if you have limited RAM and your data is huge. The cache can empty itself at an inopportune moment.
Either way, you'll need to test how your application performs with your changes. You may even find going back to the database to be the least bad option.
In addition, you could have a look at Lazy Loading some of the data, to make it less heavy.