
Greg E. answered 07/26/19
Over 20 years teaching two-semester anatomy & physiology
Aspirin irreversibly attaches an acetyl group (see below) to the cyclooxygenase enzyme, inactivating it. You're correct in thinking that, once this change occurs, it will be permanent for the life of that particular enzyme molecule. Of course, new cyclooxygenase molecules are continually being produced in the cell and if continued inhibition is desired, more aspirin must be taken.
Figure from: http://www.chem.ucla.edu/~harding/IGOC/A/acetyl_group.html