Is it incumbent upon one who commits sins to supplicate to Allah when a problem befalls him, and will his supplication be answered, or will his sins prevent that?

A Muslim is not permitted to despair of Allah's mercy, no matter how great their sins, for despair is greater than sin. The sinner must repent and seek forgiveness, and Allah accepts the repentance of His servants and forgives their sins. Obedience to Allah and uprightness are among the reasons for the acceptance of supplications. However, the door of acceptance is not closed to the disobedient if they supplicate sincerely and in distress. Even polytheists have their supplications answered by Allah if they are sincere to Him in times of hardship. The sinner must offer sincere repentance and be persistent in supplication with a good opinion of Allah, and they should know that the most worthy thing for a Muslim to supplicate for is the rectification of their religion and guidance to the Straight Path.