All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The obligatory prayers are the greatest pillar of Islam after believing in and uttering the two testimonies of faith. Whoever neglects them does not have any share in Islam. The Prophet said emphasizing the importance of the prayers, "Whoever abandons them is a disbeliever." [An-Nasaa'ee, At Tirmithi, Ibn Maajah and others] All Muslims have to observe them. The facts which the questioner mentioned like work and attending to housework, etc., are not acceptable excuses in Islam that allow one to abandon prayers. It only takes a short period during work time to perform the prayers and to implement the commands of Allaah who created man for the sole purpose to worship Him alone. However, one has to perform the prayers compulsorily during their fixed time.
Our pious female predecessors were keen to observe the prayers during their fixed times even though they used to perform the housework and probably the outside work also; they never abandoned prayers. Asmaa', the daughter of Abu Bakr, who married Zubayr all, used to feed his horse with fodder, pitch water, sew the bucket for drawing it, prepare the dough, and carry the date stones on her head from Zubayr's land which was some distance from Madeenah. She further said, "I continued serving in this way till Abu Bakr sent me a servant to look after the horse, whereupon I felt as if he had set me free." [Al Bukhari] Though she used to work very hard she never thought about neglecting the prayers, the same is true with pious women nowadays.
A Muslim woman should fear Allaah, observe her prayers, should not exaggerate in designating time for the inside or outside work. She should remind herself that she will stand in front of Allaah barefooted and naked in a Day the duration of which is fifty thousand years.
A woman is not allowed to work unless she meets some conditions as mentioned in our Fatwa: 82399.
Allaah knows best.