Praise be to Allah.
Fasting made easy
Allah has prescribed fasting and made it easy, hence Allah says in the verses on fasting (interpretation of the meaning):
“Allah intends for you ease, and He does not want to make things difficult for you.” [al-Baqarah 2:185]
Allah has permitted those who are sick not to fast in Ramadan.
Can sick people skip fasting?
The sick person for whom that is permissible is the person who has a real illness for whom there is the fear that it may be made worse or that his recovery may be delayed, or a sickness that is expected to occur because of fasting. We have explained that in the answer to question no. 12488 .
Based on this, if fasting causes the questioner to vomit or become dizzy because of physical weakness, there is nothing wrong with her not fasting in Ramadan, but she has to make up the fasts, if she is able to. If she is not able to, then she must feed one poor person for each day.
Shaykh Muhammad ibn Salih al-‘Uthaymin (may Allah have mercy on him) was asked:
What is the ruling on one who breaks the obligatory fast because of thirst?
"The ruling is that it is haram for one who is observing an obligatory fast – whether in Ramadan or making up a missed fast, or observing an expiatory fast, or fidyah – to break this fast. But if his thirst is so intense that he fears that he may be harmed or may die, then it is permissible for him to break the fast and there is no sin on him, even if that is in Ramadan, if it is so bad that he fears he may be harmed or may die. Then it is permissible for him to break the fast." (Majmu’ Fatawa al-Shaykh Ibn ‘Uthaymin, 19/question no. 149)
And Allah knows best.