If you upgrade to a custom domain for a subdomain this will not affect the AdSense on your site.
However, if you originally verified your site as a subdomain with Google Webmaster and submitted a sitemap, but have upgraded to a custom domain you will need to re-verify your site with Google Webmaster. You will also need to submit another sitemap. This will allow Google Webmaster to begin returning statistics on your new custom site.
What you need to do is remove the original Google Webmaster meta tag that you put into your home page and go back through the Google Webmaster tutorial for the new custom domain you have now published to. Here is a link to the tutorial: Google Webmaster Tutorial.