Note: This issue can still be reproduced and has been several times. It is still present in the current pre-release (1.8-pre2) and can still be tested easily with the revised test steps I have listed. The test steps I provided when this bug was last tested were more unclear, not specifically mentioning to maintain a low render distance, not specifying a distance to travel away, and not specifying which chunks to conduct the test in. I have included all those now, and hopefully it will be much easier to see.

Contents:
1. Armor Stands, Item Frames, and Paintings
Explanation
Test
Further Testing
2. Mobs
Explanation
Test

• Armor Stands, Item Frames, and Paintings:

When armor stands are placed or summoned with or without a custom name within a constantly loaded chunk (i.e. spawn chunks or entity processing chunks loaded by chunk loaders) and the player moves out of the chunks, then returning to the chunk with the armor stands, the armor stands will be unable to be seen but still be present. Armor stands become visible again upon exiting and reentering the world.

This is the same with item frames and paintings.

Occurs only in constantly loaded chunks.

Test:

1. Spawn a new world, preferably superflat so that it is easier to see, and at the exact point you spawn, place an armor stand. Record those coordinates. Set your render distance to smallest (2). (Further testing shows that render distance 2 to 5 all cause this issue if the player moves 100 blocks away and back)

2. Travel exactly 100 blocks in any direction, and remember those coordinates. Place another armor stand there.

3. Return exactly 100 blocks back in the direction of the first armor stand to find that it is gone.

4. Teleport to the armor stand(s) (for example: /tp @e[name=Bob] or /tp @e[type=ArmorStand,c=-1]) to see that the armor stands are indeed still present but completely invisible.
Teleport to item frames/paintings to see that they are present but completely invisible.

5. Travel exactly 100 blocks back to the second armor stand to find that it too is gone.

6. Teleport to the armor stand(s) (for example: /tp @e[name=Bob] or /tp @e[type=ArmorStand,c=-1]) to see that the armor stands are indeed still present but completely invisible.
Teleport to item frames/paintings to see that they are present but completely invisible.

7. Exit out of the world and enter it again and the armor stands/item frames/paintings reappear.

8. (Optional) Test with travelling more than 100 blocks from spawn, placing armor stands every 100 blocks. You may find that upon returning to the first armor stand, it is still visible, but then repeating step 1 to 4 causes it to disappear again.

Further Testing:

1. Create chunk loaders and spread them in any way you like. Make sure you make entity processing chunks by surrounding a chunk with 2 layers of chunks.

2. Repeat the very first test's procedures, placing the armor stands/paintings/item frames inside the entity processing chunks.

Further Notes: I tested this with putting one armor stand at the exact point I spawned in a new world. Then I moved 100 blocks away and placed another and kept doing this. At some point, if I move too far out then fly back to spawn, the original ones are visible still. However, if I continue and follow the test procedures again and move only 100 blocks out, they disappear again.

• Mobs

Mobs are also disappearing when the player moves away from them, but the distance the player must move from them is different. From my tests I found them to be disappearing upon moving approximately 60 blocks away and coming back to them. It seems also to only occur in always loaded chunks, but of the lazy chunk variety.

Test:

1. Create a new world, superflat is preferred to see what is occuring. Set your render distance to 2.

2. /summon <mob> ~ ~ ~

{NoAI:1b}

2. Move exactly 50 blocks straight in any direction.

3. /summon <mob> ~ ~ ~

{NoAI:1b}

4. Move 60 blocks further in the same direction. /summon <mob> ~ ~ ~

{NoAI:1b}

5. Move 60 blocks back in the opposite direction to return to second mob. /tp @e[type=<mob>,r=10] to see that it is indeed still there but invisible.

6. Move 60 blocks in the original direction to find that third mob is still there.

7. Move 60 blocks back in the opposite direction to find mob is still invisible. Continue 50 more blocks to first mob to find that it is still there.

8. Exiting and entering the world will make invisible mob visible again. Note: dropped items do not seem to have this problem.