The previous version of Push.ly did not support private user @replies but we just started working with a new Twitter API that supports this. Please let us know if you have any issues with it now.

http://blog.notifo.com/pushly-partners-with-twitter-site-streams

Just to add some info, you cannot follow protected users and get all of their tweets through push.ly due to the twitter stream restrictions, but you will be able to get their @replies to you if you are already following them.

I'm not receiving replies from protected accounts. But I do get them via Boxcar. Why?

There is currently a bug with the Twitter data stream that is preventing protected replies from coming through. We are working with them to resolve it. Boxcar uses a different method to get protected replies, but they can be delayed by several minutes. If we can't fix the bug with Twitter soon, we'll fall back to another solution.

I get replies from protected tweets. but I don't get all their tweets like I do for unprotected accounts.

Yes, there are some limitations with the Twitter Streaming API regarding protected accounts. "Direct replies" (meaning, they start with your username and are linked to one of your tweets) come though, but "indirect mentions" (where your username is in the tweet but not linked to one of your tweets) currently do not come through. We're working with Twitter on a solution to this, or to come up with another way to deliver these tweets.