What is the expiation for breaking a covenant made with Allah not to repeat a bad deed, and for not maintaining prayers at their appointed times due to extreme despair?

If what you uttered was merely a promise to abandon sin, then you must fulfill it, because abandoning sin is obligatory, and failing to fulfill a promise is a sign of hypocrisy. Repentance to Allah Almighty is due for breaking a promise, without requiring expiation. However, if you doubt whether an oath was made, then nothing is incumbent upon you, because the default is absolution of responsibility. If you took an oath or made a covenant with Allah, then along with repentance, an expiation for breaking an oath is required. Do not despair of Allah's mercy, for despair and hopelessness are characteristics of disbelievers and those who have gone astray, and repentance is accepted as long as the sun has not risen from the west or the soul has not reached the throat.