The Almighty God permits the sick people not to fast. Related verses of Surah Al-Baqarah are as follows:
184: (The prescribed fast is for) a certain number of days. Whoever among you does not fast on those days because you are sick or on a journey, then (you should fast) the same number of days on other days. Those who are able to fast are also required to pay a fee (which is equivalent to the cost) of feeding a desperate person. Whoever volunteers to do more than good (which is paying more than bound to be paid), it is better for them. If only you knew how good it is for you to fast, you would (in spite of being sick or on journey).
185: Ramadan is the month when the Quran had been sent down, that Criterion which is a guide for people and which also includes the explanatory verses of that guide. So, whoever among you witnesses that month must spend it by fasting. Whoever is sick or on a journey may fast for the same number of days on other days. God desires ease for you. He does not desire difficulty. These eases are in order that you complete the number of days and (at the end of fasting) you glorify God (during the prayer of Eid) for guiding you to this, and that you fulfill your duties towards Him.
People who have intended to fast can break the fast if they get sick. If the sick people get well, they compensate for their fast; otherwise they have nothing else to do.
One thing to know about diabetes is that insulin injections do not break the fast.