Can a woman who is experiencing non-menstrual vaginal bleeding (istihaadah) fast?

During the time when the woman who is experiencing istihaadah believes that the blood is menstrual blood, then she is menstruating and the rulings on menses apply to her. When the menses ends, then she is taahir (pure) and she should do ghusl, fast and pray and her husband may have intercourse with her, even if she is still bleeding. 

It was narrated that ‘Aa’ishah said: Faatimah bint Abi Hubaysh came to the Prophet (peace and blessings of Allah be upon him) and said: “O Messenger of Allah, I am a woman who experiences istihaadah and I do not become pure. Should I give up praying?” The Messenger of Allah (peace and blessings of Allah be upon him) said: “No. That is just a vein, and it is not menses. When your menses comes, then stop praying, and when it ends, then wash the blood from yourself and pray.” Narrated by al-Bukhari, 226; Muslim, 333. 

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said, explaining the phrase “that is just a vein”: 

This indicates that if the blood which is flowing is blood from a vein – which includes bleeding that results from surgery – then that is not regarded as menses, so the things that become haraam in the case of menses are not haraam in this case, and a woman has to pray and to fast if that happens during the day in Ramadaan. End quote. 

Majmoo’ Fataawa Ibn ‘Uthaymeen, 11/question no. 226. 

It was narrated from ‘Aa’ishah (may Allah be pleased with her) that one of the wives of the Prophet (peace and blessings of Allah be upon him) observed i’tikaaf with him, and she was experiencing istihaadah and could see the blood. Sometimes she would place a basin beneath her to catch the blood. Narrated by al-Bukhari, 303. 

See also the answers to questions no. 7501 and 5595 

And Allah knows best.