It suddenly, for no apparent reason at all, stops working until it is reinstalled. Messages are marked as being successfully sent, but they're not being received by the recipient. All my friends have the same issue.
Non-related to TextSecure, I've tried to use GCM to send notifications about faulty servers and found it quite unreliable. It seem to work fine when the phone's on and has a good WiFi connection, but seem to lose messages in real-life conditions. Not to the extent to completely stop working, just a packet loss, though.
How strange! The only issue I've seen has been to do with changing handset and needing to re-associate a phone number with a new key. There's a menu option for that which was quite well hidden.
I shall watch out for new issues as the iOS version gains functionality.
Mine almost never can properly receive MMS messages. Either I just don't get them or it can't download the attached image. It also has problems getting group messages. I've switched back to the stock messaging app.
Genuinely interested, never had issues with it so far.