Make sure your saving the data within session state and not as static, static means regardless of change on load it will revert back to the origonal value!
If your looking for that than you should be setting thoes values within the webpart properties section ;)
for session state look at my answer!
How to save variables per user session per page
for constant strings as default values (set within the webpart properties)
look at my answer here for setting properties:
sharepoint webpart property disappear after a day (C#)
session state will save your data over postback, and the webpart properties will give you default values when you first populate the webpart onto the page! each webpart can than be edited to your default value without effecting any other :)
you need to enable the session state if you get the error:
Session state can only be used when enableSessionState is set to true,
either in a configuration file or in the Page directive
goto your web application web.config file! if you dont know where it is than look in IIS manager and goto the site and goto the web application files and folders, it should be in the root folder for that web application (virtual folder).
once in you need to add the following:
<pages enableSessionState="true" enableViewState="true" enableViewStateMac="true" validateRequest="false" pageParserFilterType="Microsoft.SharePoint.ApplicationRuntime.SPPageParserFilter, Microsoft.SharePoint, Version=184.108.40.206, Culture=neutral, PublicKeyToken=71e9bce111e9429c" asyncTimeout="7">
as you can see above
enableSessionState="true" and in your case its set to false! make sure that is configured correctly!
lastly add the following if you dont have it:
<remove name="Session" />
<add name="Session" type="System.Web.SessionState.SessionStateModule" preCondition="" />
save the web.config and exit, goto the webpage and reload! bingo all works