'He is failing an exam right now' seems to make more sense, eg if the exam is ongoing. If the exam is over, the verb would be in the past tense.
Not only does it make more sense; Duo's English sentence is ungrammatical. Unless it's part of a running commentary. :)
Could you also say, "El nu reuşeşte un examen chiar acum"?
You cannot really "succed an exam," rather you can succed in passing one: reușește să treacă/ia un examen.
Duolingo, meet the present continuous/progressive tense.