How can I regain my vigor in supplicating and drawing closer to Allah, after feeling that my hopes will not be fulfilled, and that Allah does not love me and will not mend my broken heart?

You erred in losing hope in the answer and feeling that God does not love you; these are devilish whispers. God answers the supplication of His servant if the conditions for the answer are met and its impediments are absent, either by hastening the answer, or by storing it as good deeds, or by averting an equivalent evil, in fulfillment of His saying, Exalted is He: "And when My servants ask you concerning Me, then [answer them], I am indeed near. I respond to the invocation of the supplicant when he calls upon Me. So let them respond to Me [by obedience] and believe in Me that they may be [rightly] guided" and "And your Lord says, 'Call upon Me; I will respond to you.'" The conditions for an answer are met by responding to God's commands and prohibitions and believing in Him. Among the impediments to an answer are haste and abandoning supplication. One must respond to God, believe in Him, trust in His promise, and supplicate without haste, beginning the supplication with praise of God and blessings upon the Prophet, peace be upon him, and ending it with them.