Is a single expiatory offering (kaffarat yamin) sufficient for repeatedly delaying Fajr prayer after making a vow, and does this fall under the category of a "vow of obstinacy" (nadh al-lajaj), and is expiation due every time the prayer is delayed, even if one is unable to pay?

The basic principle is the obligation to fulfill a vow, as Allah Almighty says, "And let them fulfill their vows," and as the Prophet, peace and blessings be upon him, said, "Whoever vows to obey Allah, let him obey Him; and whoever vows to disobey Allah, let him not disobey Him." However, the vow mentioned is a "vow of obstinacy" (nadhir lajaj), and its maker has the choice between fulfilling the vow or offering an expiation for an oath (kaffarat yamin).

The expiation for an oath is: feeding ten poor persons from the average of what you feed your own families, or clothing them, or freeing a slave. And whoever cannot find [the means], then fasting for three days.

If your intention was for the vow to be repeated with each instance of delaying prayer, then you owe a hundred [dirhams] or an expiation for an oath for each delay. If you cannot find [the means] to feed or clothe, then you must fast three days for each breach. However, if you did not intend repetition, then you owe only one expiation.