*VERSIONS 1.7.4-.9 UPDATE YOUR AFFECT LINE ABOVE*

When I go 100 or less blocks from my horses and donkeys they occasionally disappear. No, I do not believe they have just walked off.

Steps to Reproduce:
1. Tame a horse of donkey
2. Step 20-80 blocks away from them horizontally or vertically
3. Wait 2-3 day/ night cycles
4. Observe if they simply just "walk off"
5. Your horse should be nowhere to be found