What should I do when I draw near to Allah and then drift away, and what about this weariness that I feel?

What you are suffering from is a weakness of faith. Strengthen your faith by knowing Allah as He ought to be known, for the most God-fearing among people are those who know Him best. Avoid the causes of weak faith mentioned in Fatwa No. 35182. You should also engage in the remembrance of Allah, recite the Quran, and make supplications. The Messenger of Allah, peace and blessings be upon him, said: "Indeed, faith wears out in the heart of one of you just as a garment wears out, so ask Allah to renew faith in your hearts." He also used to supplicate frequently: "O Allah, Turner of hearts, keep my heart firm upon Your religion."