What is the ruling on one who commits adultery while married, then repents and returns to adultery, while maintaining prayer, and how does acceptable sincere repentance occur?

Adultery is among the gravest of major sins. Allah has coupled it with polytheism, and the Prophet, peace and blessings be upon him, clarified its danger to faith. However, Allah accepts the repentance of the penitent if it fulfills its conditions: abandoning the sin, regretting it, resolving not to return to it, and restoring rights to their owners if they pertain to financial rights. Whoever is afflicted by this should possess sincere will, seek help through supplication, maintain prayer, avoid incitements such as unrestrained gazing and mixing, and contemplate the punishment for indecency.