You need to enable Elmah for remote access by adding the following configuration setting to the <elmah>
section in your web.config file. The default setting for this value is false, which only allows localhost, hence why it is working on your local machine from within Visual Studio.
<elmah>
<security allowRemoteAccess="true"/>
</elmah>
I always seem to forget this myself and spend a few minutes scratching my head 😉