В браузере отключаются куки, а не сессия, сессия хранится на сервере ,куда и надо сохранять переменные и пользоваться ими, это стандартное решение проблемы.

ИЗ МСДН

ASP.NET provides the following support for sessions:

A session-state facility that is easy to use, familiar to ASP developers, and consistent with other .NET Framework APIs.

A reliable session-state facility that can survive Internet Information Services (IIS) restarts and worker-process restarts without losing session data.

A scalable session-state facility that can be used in both Web farm (multicomputer) and Web garden (multiprocess) scenarios and that enables administrators to allocate more processors to a Web application to improve its scalability.
A session-state facility that works with browsers that do not support HTTP cookies.

A throughput equivalent to that of ASP (or better) for core session-state scenarios (50/50 read/write when putting items into shopping carts, modifying last page visited, validating credit card details, and so on).