How long does swelling in one leg associated with deep vein thrombosis last?

Persistent. Depending upon the severity/extent of the dvt, and the treatment methods, the swelling can be minimal to severe, lasting weeks, to months, and years. The post thrombotic swelling can be lessened by using appropriate anticoagulation, compression hose, thrombolysis when indicated.
Swelling. The swelling will start to improve as the vein clot resolves,or as other veins of the superficial system take over the work load.