You can write an ADF Cartridge for this. In this ADF cartridge, you can read/write data to the claimstore, perform any action on these values, so you could store or retrieve them from/to the database. An example can be found here : https://github.com/jhorsman/weather-cartridge and here http://erichuiza.blogspot.be/2012/07/ambient-data-framework-in-nutshell.html
These cartridges are written in Java, even if you consume them in your .NET web application.
Some difficulties you might encounter:
you need to find a way to map a user with the data stored in the DB. If your users are authenticated, then you can use their user ID. If not, you should put some persistent cookie on the client's browser, and put the value of this cookie in a claim as well, so you can identify which user is currently active
you should keep track of which values are saved in the DB. You should only store them in the DB if they are new or modified, as you don't want to write to your DB on every request (the cartridge is run on every request)