Is it permissible to continue supplicating for a specific girl to be my destiny, when she has been forced to become engaged to someone else whom she does not want?

If the girl's guardian agrees to the suitor but she rejects him, then her word is binding. It is permissible for her to be proposed to by another, because she has a right over herself, and her rejection negates her guardian's approval. If you are unable to marry her, then look for someone else and entrust your affair to Allah, for it may contain good for you, as (No disaster strikes upon the earth or among yourselves except that it is in a register before We create it—indeed that, for Allah, is easy— In order that you not despair over what has eluded you nor exult [in pride] over what He has given you. And Allah does not like every self-deluded and boastful one), and (But perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah Knows, while you know not).