For some days now the "Replies" tab on Twitter has been inactive. Try to use it and you get the message that "Twitter is stressing out a bit right now, so this feature is temporarily disabled".
This means that if anyone has replied to one of your tweets (in my case using @denniswright in the text) I will only see it in my Twitter timeline if I happen to follow them. Now most of the tweets aimed at me are from people I do follow so it's not a massive issue for me. It's more of a problem for Twitter heavy hitters who are followed by a shedload of people, while themselves following relatively few, but wanting to check on interesting tidbits from their hinterland of followers.
The latest tweet from John Dvorak, 23 hours ago, read: will REPLIES EVER work again? Looks sketchy. Makes it hard to interact.
A simple solution is to use Summize.com as a stand-in for Twitter Replies. There are any number of Twitter-related websites that fill in the numerous gaps in Twitter's functionality, taking advantage of the fact that at least Twitter exposes a decent API. Summize contributes the much needed search function, so if I search in Summize for @denniswright I will get all tweets directed at me, including replies from followers who I don't follow back.
I hope John Dvorak and other Twitter heavyweights (not being personal here John) know about this or figure it out soon.