Coumadin/warfarin is notorious for the difficulty in keeping your levels in range. Coumadin is known for having many drug-drug and drug-food interactions, which can make you over or under coagulated. For instance, since it works by being a vitamin K antagonist, foods that contain vitamin K (like leafy greens) can lower your INR. Taking vitamin E or fish oil or aspirin could raise it, and make bleeding more likely.
Coumadin along with other blood thinners can cause this. Coumadin is a strong blood thinner.