Lost a GBB almost the exact same way. It's hard to tell with a T being sick/in need when you're new. I'm sure Jeff and Alexa and a few others know immediately when something is starting to go awry. I was also told that mortality rates for slings can be high. I'm lucky to have only lost one out of the 8 I've kept. I know GBB are usually pretty hearty but mine did almost the same thing as yours until I realized it was dead. Hope this isn't the case but good luck!
Regards,
B