If you are unable to chat on a liveshow you have most likely been banned from a liveshow. 

There are two possible explanations:

Either you have accumulated a large number of alerts issued by different members or by the broadcaster himself during the live shows (due to language abuse or a high rate of posts in the chat for example).

Or you are one of the ignored usernames of this member and the broadcaster himself has chosen to exclude you from his Exhib show.