In Antony and Cleopatra, can we say that Cleopatra's age and her past experience of love with Ceasar turned Antony's romance into tragedy?
I don't think either her past experiences or age has anything to do with turning Antony's romance into tragedy.
Antony is a man caught between his duty, which includes marrying Octavia, and his passion for Cleopatra. One has only to look at Enobarbus's purple passage about their first meeting (Act II, scene 2) to understand. When Maecenus suggests that Antony must leave the Egyptian Queen, Enobarbus replies, "Never. He will not. / Age cannot wither her, nor custom stale / Her infinite variety..."
Ironically it is his love for her that destroys him. Rather than trusting his own understanding of warfare and strategy from personal experience, he caves into Cleopatra who insists they fight by sea which proves to be disastrous.
He believes the message that she is dead and like Cleopatra, he does not want to be taken to Rome as a captive. For this one time ruler of a third of the Roman Empire, it would be too humiliating. A Roman captive Cleopatra would also be too humiliating for this proud woman.
There was no other possible outcome for the two lovers caught up in a highly political world. Their only chance to be together was in death.
"She shall be buried by her Antony. / No grave on earth shall clip in it / A pair so famous...."