Angirasa first says
As regards Brahmanas and Kshatriyas, fasts for three nights at a stretch are ordained for them. Indeed, O chief of men, a fast for one night, for two nights, and for three nights, may be observed by them. (They should never go beyond three nights).
Then
That man who passes a whole year observing fasts for five days and taking food on only the sixth day, acquires the merit of the Horse-sacrifice.
Then again...
No fast for more than a month has been ordained. Even this is the ordinance in respect of fasts that has been declared by sages conversant with duties.
So, is it allowed to fast more than 3 days together?
