All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Your mother is obliged to do many things:
1- She is obliged to repent if she deliberately broke the fast without any sound religious reason. To deliberately break the fast in Ramadan is a great major sin which requires repentance.
2- She is obliged to make up for any days she failed to observe the fasting and pay a compensation for each day. The compensation (for feeding a person) is 750 grams of food for each day she broke the fast if she delayed making up the days she broke the fast while being able to make them up from previous year to the year after it; and this is what appears from the question.
3- If a trustworthy doctor rules that she became unable to fast due to this disease and that this condition of being unable will continue and she is not expected to be cured from it, then she will not be obliged to make up the numbers of days she broke the fast but she is obliged to give another compensation instead of making up the days she broke the fast-according to the number of days she broke the fast. Imaam An-Nawawi stated the same thing for a person who dies and did not observe fasting, as he said: 'If a person delays making up the days he broke the fast while being able until he dies after the commencement of Ramadan before he makes them up, his heirs are obliged to give a compensation on his behalf. There are two well-known opinions on this issue. The most correct opinion according to the Shaafi'ee school is that his heirs are obliged to give compensation twice; 750 grams of food for breaking the fast and another 750 grams for delaying to make up the fasting in due time. Al-Maawardi said: "This is the view of the Shaafi'ee and the opinion of all the scholars of the Shaafi'ee school with the exception of Ibn Suraij.'
4- Now she is like a very old person, she is not obliged to fast but she is only obliged to pay compensation according to what we have already explained.
As regards your question to whether or not she is able to fast on this condition, the answer is that if a trustworthy doctor informs her that her life will be in danger if she does so, then it is not permissible for her to fast.
As to whether Allaah will forgive her or not if she repents and seeks His Forgiveness, then this is a matter that only Allaah Knows but she should know that Allaah forgives all the sins. Allaah Says (which means): {Say, "O My servants who have transgressed against themselves [by sinning] do not despair of the mercy of Allaah. Indeed, Allaah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful."}[Quran 39:53].
For more details please refer to Fatwa 89510.
Allaah Knows best.