Lost credit on air for being dogmatic (11)
I believe the answer is:
doctrinaire
'dogmatic' is the definition.
(thesaurus)
'lost credit on air' is the wordplay.
'lost' indicates an anagram.
'credit'+'on'+'air'='creditonair'
'creditonair' anagrammed gives 'DOCTRINAIRE'.
'for being' is the link.
(Other definitions for doctrinaire that I've seen before include "Dogmatic" , "Trying to impose beliefs" , "Seeking to impose a view" , "Impractical theorist" , "not practical" .)