Why do asthmatics have less air capacity than normal people even when they are not having an attack?

Air trapping. One of the big problems with asthma is that air is trapped in the lungs. When this happens, you can breath in just as much or more than a healthy person but you can't breath all the air out. As this air collects in the lungs, the total lung volume exposed to fresh air diminishes, causing some of the symptoms of asthma.
Chronic disease. Asthma is a chronic inflammatory disorder of the breathing tubes that flares up periodically. At those times lung capacity decreases noticeably, sometimes dramatically. Lung function returns to normal between flares in patients with intermittent or mild persistent asthma. In those with moderate or severe persistent asthma lung function improves but does not return to normal between flares.
Persistent disease. Many asthmatics walk around with persistent inflammation in their lungs. They are so used to feeling ill that they don't recognize the illness for what it is. This is a dangerous situation which can be reversed with aggressive medication management. Left untreated it can result in sudden death from an asthma attack.