Mobs ride in carts by the way. Perhaps your carts are disapearing from a station which is accessible by hostile or passive mobs?|
I have a track with two ends at one end. One of them is up a very high tower, the momentum from which powered the cart for a long time until I found enough gold. The second one is at the bottom of the tower, just sittin on the grass. A cart left at the top one never seems to wander off but the bottom one, even though it has to go up a one-block slope, tends to disappear. I had read about mobs riding carts before and did finally see a pig get in and ride it away.