Code:
http://streams.altazip.com:8000/kmgr
http://streams.altazip.com:8000/kmti
I just tried this at work as well, and it stops here as well.
I usually do nothing after I begin streaming and then recording a particular program, thinking it might hinder the process.
I also called the station and asked if it would be OK to stream and copy, and they encourage it.