It sometimes brought the tweets, but mostly not.
I did, what you recommended. Then immediately retrieved the tweets, then I tried to reply to another person - same thing again.
First the problem was with Plume, now I moved over to official Twitter app. I even had problems with logging in to Twitter over 3G with official Twitter app, although I had no problems with downloading it from Market.
I also kept an eye on data indicator in the status bar. It shows, that data is moving over H/3G both ways, while trying to send a tweet.
Oh, and my internet should be around 2Mbps download and 384kbps upload. Haven't had problems with slow internet earlier.
The last tweet, that I tried to send. It took about 10 minutes and then it showed, that tweet couldn't be sent. I went over on Wifi and then it went through.