Is stopping praying for the cure of a specific illness – due to its negative impact on one's psyche and certainty – considered a sin, even though the patient feels psychological improvement after ceasing to pray?

You are not definitively sinful if your interruption of the supplication was not out of despair of Allah’s mercy, for supplication is commendable, and its abandonment does not lead to sin. However, abandoning supplication due to becoming disheartened and impatient is one of the impediments to its acceptance, as the Prophet, peace and blessings be upon him, said: "The supplication of any one of you will be answered as long as he does not pray for a sin or for the cutting off of ties of kinship, and as long as he does not become impatient." And he explained impatience by saying: "He says: 'I have supplicated, and I have supplicated, but I do not see that it is being answered for me,' so he becomes disheartened at that point and abandons supplication." Thus, whoever becomes impatient and finds the answer slow in coming, then abandons supplication, is like one who abandons his planting before it reaches fruition. The supplicant should let hope outweigh despair, for Allah will either answer him, or avert a calamity from him, or store up the reward for him in the Hereafter. So, supplication is an act of worship that should not be abandoned.