Perhaps one of the reasons this has remained unanswered is that it is not clear as to what you mean by a defective tragedy.
Do we have a protagonist? Yes. In this case it is both Antony and Cleopatra. Are they of high status? Cleopatra is the Queen of Egypt, a conquered nation, but a queen none the less. As a member of the triumvirate, Antony is ruler of one third of the emerging Roman empire.
Are these two people flawed? Definitely. Cleopatra seems to be a woman ruled by her emotions. She is use to having her way. Her pride is part of her charm but it is also her downfall.
As for Antony, he wants to have it both ways, Rome and Cleopatra. His pride has carried him this far and he wants to believe that somehow he will pull it off.
Does the situation in the play go from good to bad? I'd say the defeat of the title characters to the Roman army and death of these two at their own hand rather than be taken in captivity back to Rome is bad.
Despite the fact the play is named for the two lovers, we rarely see them alone together. They are always in a public situation. It is only through death and meeting up in the next world can these two be together.
I'd say that that meets the criteria for a tragedy.