Yes, since inhalers contain medicine, they will break the fast. If a patient has asthma then their difficulty in breathing is a good indication that they should break the fast and use the inhaler if there is a flare up and make up one fast later as qadha. Therefore, if your doctor feels that your condition is severe enough to cause weakness or worsen your health if you fast then this could be considered a chronic illness which will allow you to break your fast and pay fidy?h. If you recover from your illness then you will need to perform make up the fasts (qadha). (Ramadan aur Jadid masa'il pg.141)