Turkish High Committee of Religious Affairs has the following opinion about the usage of these sprays:
The dosage of the sprays used by the patients of lung disease is not more than 1/20 ml, which is a very small amount. Considerable part of this dose is absorbed by the inner surfaces of the mouth and the bronchioles. There’s no scientific evidence to prove that the rest of the medicine reaches the stomach through saliva. Even though it reached the stomach, it is a much smaller amount than the amount of water that remains in mouth during ablution. This is important, because there is a hadith (Darimi, Sawm, 21) regarding the case that the water remaining in mouth during ablution and reaching the stomach, shall not break one’s fast. There’s also the consensus (ijma) of Islam scholars on this subject.
Additionally, it is inevitable that tiny particles and inconsiderable amount of chemicals reach the stomach after using miswak, too. It is expressed in respectful hadith resources that the Prophet Muhammad (p.b.u.h.) had used miswak during his fast.
Besides, the following rule always applies: “certainty is not overruled by doubt”.
From this point of view; if the asthma patients have no other sickness to prevent them from fasting, oral sprays that ease inhalation with the content of oxygen shall not break their fast.