Is it permissible for a woman to pray despite mucus discharge from her all day long, even with her attempts to bathe to be clean?

It is permissible, rather obligatory, for one from whom saliva or mucus issues to pray the prescribed prayers at their appointed times, because neither invalidates ablution, and both are pure. The Prophet, peace and blessings be upon him, permitted the worshipper to spit into his garment or beneath his foot during prayer.