The css you were trying to apply for link visited wont be persisting after the postback as we used to do it for a hover.
you should try to change it using Javascript/Jquery or in the code behind as below .
protected void LinkButton1_Click(object sender, EventArgs e)
{
LinkButton lb = (LinkButton)sender;
lb.ForeColor = System.Drawing.Color.Purple;
}
<asp:LinkButton ID="LinkButton1" runat="server" ForeColor="Black" OnClick="LinkButton1_Click">My Link Button</asp:LinkButton>
Hope this helps...