I don’t check very often my twitter to know when someone replies and I find it hard to figure out what’s going on when i check a couple of days after even using a client showing only the reply (my client of choice lately is the Emacs twittering mode client)
I have made a script who’s checking your direct reply and email it to you. This is to setup via a cron on a server who has a mail server configured locally. You can get it from here :