If a person is predestined for hardship, will he remain so until the end of his life? And what is the wisdom behind Allah's delay in answering the supplication of someone in dire need of relief?

Allah the Almighty is All-Wise. He only delays the answer to a supplication for a profound reason. Every supplication made by a servant is good for him and is answered, but the form of the answer varies according to Allah's wisdom. Either the requested matter is granted, or Allah diverts an equivalent evil from him, or He stores its reward for him until the Day of Judgment. Continue supplicating with certainty and good expectation of Allah, and know that what He ordains is good, and that supplication is a means of achieving what is desired and repelling what is feared. Furthermore, disobedience to Allah, especially abandoning prayer, is among the causes for the delay of good. So, praise Allah for guiding you to observe prayer, and seek good from Allah, and beware of despair, and persist in obeying Him and supplicating with certainty that all good is in Allah's hands.