|Telephone lines don't have the same limiting factors as network cables so the issue can't be the length of the phone line.|
The only things I can think of that may (and I stress "may") affect this is whether or not that extension socket is wired correctly, and possibly, the device it connects to (likely some sort of panel that allows multiple extension connections to connect to the one active phone line coming into the house) has a bad connection.
You can test the phone line by plugging a phone in. If the phone doesn't work, then you know there's a problem with it. Barring that (ie: the phone works) you can check the panel at the other end of the phone line and see if there's any obvious physical issues with it. If not, trace the socket that works fine and swap the wires from the extension that isn't working fine with the wires from the one that is and see if that doesn't fix the issue.
If none of the above does the trick, you might want to call your telephone company and have them come have a look.....but keep in mind, they'll charge you.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.