Should one stop supplicating when one sees that one's state combines good fortune and trials?

The question is not clear. However, if it is about abandoning supplication (du'a) because it has not been answered, then this is forbidden. For Allah answers the supplicant as long as he does not become impatient and say, "I supplicated but was not answered." And answering is broader than granting the request; it may be by averting evil or by storing it for the Hereafter. One should not be impatient and abandon supplication. If the matter is unclear, one should perform the Istikhara prayer.