Fasting continually means that a person fasts for two or more days without breaking the fast, i.e., the fast continues all night and the person does not eat or drink.
The Prophet (peace and blessings of Allaah be upon him) used to fast continually, and Allaah gave him the strength to do that, but he forbade his ummah to do that out of compassion and mercy towards them.
Al-Bukhaari (7299) and Muslim (1103) narrated that Abu Hurayrah (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) said: “Do not fast continually.” They said, “But you fast continually.” He said, “I am not like you. I spend my time with my Lord and He gives me food and drink.” They did not stop fasting continually, and the Prophet (peace and blessings of Allaah be upon him) fasted continually with them for two or three days, then they saw the new moon, and the Prophet (peace and blessings of Allaah be upon him) said: “If the new moon had come later I would have continued my fast” – as if to prove to them that they were not like him and could not continue fasting.
Ibn Qudaamah said in al-Mughni, 4/436: Continual fasting is makrooh according to the majority of scholars.
Al-Nawawi said in al-Majmoo’, 6/357:
With regard to the ruling on continual fasting, it is makrooh, and there is no difference of opinion among us concerning that. But is it makrooh in the sense of being forbidden or makrooh in the sense of being disliked? There are two opinions concerning that … (the more correct of which) according to our companions and the apparent meaning of the statement of al-Shaafa’i is that it is makrooh in the sense of being forbidden.
Shaykh Ibn ‘Uthaymeen said in al-Sharh al-Mumti’, 6/443:
It appears that the ruling with regard to continual fasting is that it is haraam.
And Allaah knows best.