I came down with diarrhoea in the morning and it did not stop, and I felt the impact of that in the form of pains and cramps; I lost a lot of fluid and I felt exhausted. Should I carry on fasting?

Praise
be to Allah.

Allah, may He be exalted, has granted a
concession allowing the sick person for whom it is difficult to fast to
break his fast and make up the days when he did not fast. Allah, may He be
exalted, says (interpretation of the meaning):

“and
whoever is ill or on a journey, the same number (of days which one did not
observe Saum (fasts) must be made up) from other days. Allah intends for you
ease, and He does not want to make things difficult for you”

[al-Baqarah 2:185]

The kind of sickness that makes it
permissible for the fasting person to break his fast is the kind of sickness
that makes it difficult to fast, or that makes the sickness worse, or will
delay recovery as a result of fasting. For more information, please see
fatwa no. 12488 

Shaykh Ibn ‘Uthaymeen (may Allah have
mercy on him) said: 

The situation of the one who is sick may
be of different types: 

1.    

Cases that are not affected by fasting, such as a slight
cold, a mild headache, toothache, and the like. In such cases it is not
permissible for him to break the fast.

2.    

Cases where it is difficult for him to fast, but it will
not harm him. In this case it is makrooh for him to fast  and it is Sunnah
for him to break the fast.

3.    

Cases in which it is difficult for him to fast and he
will be harmed by that, as in the case of a man who has kidney disease,
diabetes and the like. In such cases, it is haraam for him to fast. 

End quote from ash-Sharh al-Mumti‘
(6/341). 

Based on that, if the diarrhoea is mild,
and will not affect the fast or cause exhaustion or undue hardship, then it
is not permissible for the fasting person to break his fast, and he must
complete his fast. 

But if the diarrhoea is severe, to the
extent that the fasting person feels tired and exhausted, then he has to
break his fast. The person who suffers diarrhoea needs to make up what his
body has lost of fluids and salts, and if he does not do that, then he is
exposing himself to the risk of severe exhaustion. 

If the diarrhoea is even worse than that,
in the sense that if he does not take medicine to stop this diarrhoea and
replenish the fluids and salts that his body has lost, there is the fear
that he will suffer harm, then in this case he must break his fast and it is
haraam for him to carry on fasting. 

But then he has to fast a day to make up
for this day, after Ramadan ends. 

To sum up: so long as the diarrhoea has
reached the stage of causing tiredness and exhaustion, it is mustahabb for
you to break the fast and it is makrooh  for you to carry on fasting in the
face of this hardship, and you should make up that day later on. 

We ask Allah, may He be exalted, to heal
you. 

And Allah knows best.