It seems that the URL http://stable.toolserver.org/editcount (note, no trailing slash) is returning a 302 redirect to http://localhost:4880/editcount/, which is obviously not going to work. The URL http://stable.toolserver.org/editcount/ with a slash works fine, though.
Also, I tried to report this issue on JIRA (https://jira.toolserver.org/), but it seems my account (vyznev) can only create issues on the "Account Approval" project, even though I've successfully files issues on other projects in the past.
Also, the JIRA link on the stable editcounter page points to the old URL https://jira.ts.wikimedia.org/browse/EDITCOUNTER, which gives a big error message about an expired and invalid SSL certificate.