Does the mere recollection by the repentant fornicator of his sin and indulging in some lust for a few moments, followed by seeking forgiveness, indicate that his repentance has not been accepted, and is he required to renew his repentance?

Contesting sin then restraining it through repentance does not invalidate it. A person's repentance is sound, and they are not required to renew it. What occurs in their heart concerning this does not harm them; rather, they must strive against their soul and cast away such thoughts. Indeed, guarding one's thoughts is among the greatest duties of those brought near to Allah.