Horse missing when I log in

Every time I ride or hold a horse with a lead rope when I save Minecraft, the horse is gone when I go in to the world again. I have lost two of my best horses this way, and I am stuck far away from my house having to walk by foot all the way back. Sometimes the game glitch when I ride too, and I am being thrown out of the game. The horse is then gone when I go in again. 
This is making me want to stop playing and I hope you can fix it.