There could be an error in that template. If there is an error within the template you have just saved there will be an error when that template is compiled for client side use. For a template to be used on the client side the Smarty template system pre-compiles that template to help page load times. If at that time that template has any errors within it and there is a current pre-compiled template already in use that will stop that new template from being compiled. The system overwrites the old pre-compiled template with the new one if there are no errors. If the new template has errors it can't be pre-compiled and can't overwrite the old template. Thus the old template stays "in view" on the client side making it look like your changes haven't had an effect. Your changes are still in that template within the admin tool if you look though. Look through your template to see if you can find and fix that error. If the error eludes you there is another way to force use of that template and have the system discover the error for you.
The next step is where a test installation of the software to test these issues on before going live would help. You could force the change there and throw the error on the client side but only you would see the issue. But if you don't have that testing installation you can still force the error to display in your only installation. But if your site is live you may want to turn it off while you work this issue out. You should still be able to view it as the admin.