Aspirin in low doses produces long lasting inhibition of platelet cyclooxygenase because:

Aspirin in low doses irreversibly inhibits COX enzyme in platelets and the endothelium. Platelets lack nucleus and thus cannot regenerate COX whereas endothelium can synthesize fresh enzyme. Net effect of this process is the inhibition of platelet cox and thus, TXA2 synthesis. Low TXA2 level results in the anti-aggregation of platelets.