What is the way to overcome feelings of apathy, sadness, self-blame, and frustration after repeatedly facing closed doors despite performing Istikhara, and what can strengthen and aid her?

Istikhara is a delegation of affairs to Allah, so that He may choose what is best for His servant, and its most important benefit is contentment with what Allah has decreed. Recall the verse: "And perhaps you dislike a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah knows, while you know not." It removes the whispers of Satan that aim to instill sadness. Satan is keen to sadden a person and corrupt their religion. The solution is to turn to Allah with sincerity, seek refuge in Him, and turn away from whispers. Continuing in obedience, remembrance, and listening to admonitions helps repel the schemes of Satan and achieve one's goals, in accordance with His saying: "And whoever fears Allah - He will make for him a way out And will provide for him from where he does not expect." There is no harm in seeking employment with patience and seeking help from trustworthy people, and you are in a good state with a woman's decision to stay in her home.