What should one do if, after proposing, he was rejected without a reason, yet he still desires the girl, and he has prayed Istikhara many times, being certain in his heart that she will return to him, but the reality is otherwise?

If you sought Allah’s guidance (Istikhara) and the marriage to a specific girl did not materialize, then know that this is good for both you and her. Allah averts evil and chooses what is best for His servant. Ibn Mas’ud said that Allah might turn away an affair that He had made easy for a servant if it contains his destruction. What you feel towards that girl is a probable matter that should not be clung to. Instead, ask Allah for what is good, and seek a woman of character and religiosity, and do not delay marriage. You should ask Allah to facilitate your marriage to a righteous woman, strive to find her, avert your gaze from the previous girl, believe that good lies in what Allah has decreed, and do not grieve over being rejected.