When i duplicate an audio track that has Record enabled, the new track does not have the Record Enable on…
I do have ticked the “Enable Record On Selected Audio Track” … 
Win 7 64, Cubase 7.0.4
“Enable Record On Selected Audio Track” does exactly that - ergo, you need to select it to enable the record.
Personally I hate this function and always have it turned off - preferring manual control over this.
Perhaps Ctrl-C Ctrl-V would give you better results (assuming you’re using the Duplicate function) - sorry I can’t confirm at the moment.