For your convenience we use so called "flash cookies" to store some configuration information between sessions. Specifically the radar configuration and graph visibility settings.
It appears that you have disabled the storing of such cookies.
If you disallow third party storage then these settings will not be kept between sessions.
If you'd like to you can re-enable the storing of this information by going to the Flash Global Storage Settings and checking the box "Allow for third-party Flash content to store data on your computer". You'll need to restart your browser after making that change for it to take effect.
You can also access the settings by right-clicking on the application when viewing it. This allows you to configure both the global settings and per-application settings (for the curious there's more than storage to configure).
There is no harm in disallowing the storing of this information, other than the annoyance of having to reconfigure the application each time you use it.
We also store some configuration information in the regular browser cookie (most recently used locations and your Fahrenheit/Celsius settings) - if you have turned off those cookies then that information will also be lost.
A recent update to Google Chrome changed their policies with respect to storing flash cookies.
We are working to resolve this issue, but in the meantime you can make an exception for cookies from "weatherspark.com".