Basically, command blocks are destroyed when the Enderdragon flies through them. Considering the purpose of command blocks, I think it's a safe assumption that anything other than a player in Creative mode being able to destroy one is a bug.
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@Michael Norton: To set Command blocks not to be destroyed would be only the tip of the iceberg, you would have to make restone dust, comparators, repeaters, restone torches, pistons, hoppers, etc. also indestructable...
See MC-46591.
Isaac, ahem.
Kumasasa's word:
To set Command blocks not to be destroyed would be only the tip of the iceberg, you would have to make restone dust, comparators, repeaters, restone torches, pistons, hoppers, etc. also indestructable...
No, because all of those redstone related items are available is survival, so they wouldn't be indestructible (end stone and obsidian violate that, but that's because it makes sense gameplay-wise for them to be unbreakable by the dragon - they both come from its home dimension). Command blocks and barriers are creative-only, so they should be unbreakable. While it's true that without the redstone items available, it would be harder to make useful constructions, plenty can be done by setblocking redstone blocks, which would still work. Command blocks are also un-mineable and un-explodable, which contributes further to the assumption that they should be completely indestructible.
Actually, this has been fixed for 1.8 already (MC-64571).
The ender dragon can destroy any blocks. It would have been too difficult to make them not do that.