I believe that your problem is that you're adding the link in the auto-generated designer file. You can't predict when Visual Studio will modify/recreate it, and what changes it will have. In my case, the same statement you use gets replaced by:
this.linkLabel1.LinkArea = new System.Windows.Forms.LinkArea(1, 1);
The workaround is simple enough. Place:
this.linkLabel1.Links.Add(1, 1, "www.google.com");
In the Load
event of your form. Also make sure to remove from the designer region all the unwanted parts of the code which have been refactored by Visual Studio.