How long can a blood clot stay in the location where it developed if on blood thinners?

Long enough: Once the blood clot has formed it is stable and should not be affected by blood thinners, it will stay in place normally unless it is disturbed mechanically . If it bleeds you need to seek professional advice.

You are safe: Once the clot has formed, just be careful not to do anything that will dislodge it. It is an important part of the healing process. Avoid vigorous rinsing or spitting, no smoking, no hot liquids and don't blow your nose. A recent study just published shows that many dental procedures can be safely done on warfarin. Hope it helps.