Changing the state of anything isn't permanent unless you specifically code for it to be.
The best way to handle this would be to add a setting:
1) Open your projects Properties in the solution explorer, and double click on "Settings.settings"
2) In the resulting grid, change the Name to "MySetting", and set the Value to "Defaulted value". Leave Type and Scope as "string" and "User" respectively.
3) Save and close the settings window.
4) To read your setting:
string s = Properties.Settings.Default.MySetting;
5) To write your setting:
Properties.Settings.Default.MySetting = "My new setting value";
Properties.Settings.Default.Save();
Then add code to the form save and load methods to use the saved setting and update the visible status of your checkbox in the form Load and Close events.