Can she refuse her husband’s request for intercourse if she knows that he will miss Fajr prayer?
Falling short in performing the obligatory prayers and delaying them until the time for them is over is a major sin, and the one who does that habitually and takes the matter lightly is in grave danger. It will lead to his doom in the Hereafter and to his being a loser before Allaah.
The wife must also help her husband to obey Allaah and help him to avoid sins as much as possible, with kind words and beautiful exhortation, and by using the means that are prescribed in sharee’ah, not those that are forbidden.
If you can agree with your husband upon a time after which you will both be able to offer the prayer on time and regularly, then that is best.
Otherwise, you do not have to do anything other than advising him, and helping him to pray by dealing with him kindly and gently. If he responds, then praise be to Allaah, otherwise he is the one who will bear the sin, not you. It is not permissible for you to refuse to share his bed if you know that he is falling short. Every accountable person must bear the consequences of his actions, and will be asked about what his hands have earned – no one else.
Moreover, if there is something that keeps the husband from attending prayer in congregation, this is a sin, but it is less serious than his failing to offer the prayer at the proper time. The sin in that case is serious, if the person did it deliberately.
Whatever the case, we ask Allaah to guide you and accept your deeds, because we can see that you care about your and your husband’s prayer. We ask Him to fill all the Muslims with love for Him and hope in Him and fear of His punishment.
And Allaah knows best.