Did you get any error messages when publishing the site ?
The FrontPage hit counter has to be published to a web server that has the FrontPage Server Extensions, SharePoint Team Services v1.0, or Microsoft Windows SharePoint Services 2.0 installed.
Assuming you managed to publish the site without any error warnings about FrontPage Extensions or similar, have you tried refreshing the page in your browser ?
Sometimes all you need to do is refresh the cached copy of your page (click the Refresh button or use Ctrl+R) to see the adjusted counter that reflects the number of visitors.
On a purely personal note, I detest hit counters with a passion that borders on the rabid. They serve no useful function. If you or your client want accurate statistics about your visitors, your web host will offer them via Webalizer or a similar site stats application. If your site gets little traffic it doesn't look good to tell the world that you have had 92 hits, just to put a number on it for the sake of argument, while a busy site normally looks like one without its visitors being told that it is one.
Anyway, I've gone off on one...
Check and double check your browser cache by using the refresh option and then make sure when you publish your site that there are no error messages about missing FontPage Extensions.