Sometimes villagers don't breed even when all conditions are met. I'm providing a link to my survival world download from realms.

These villagers were kidnapped from the naturally generated village. There are definitely no other villages or villagers within more than 100 blocks. I gave them several stacks of carrots via droppers and they've picked them up. I've traded with them dozen times. I've moved doors close to them, the doors are valid. Waited about an hour. Nothing helps.

When I've switched to the creative mode in the same copy, removed this two villagers and created two another via eggs at the same chamber, they started to breed immediately after I have given them carrots. What is the difference?

The same behaviour sometimes occurred when I was testing this design in creative testing world: the villagers breed as expected for some time and then without any visible reason they stop and I have to replace them with the new ones.

This definitely looks like a bug.

Please check out the provided world download. The artificial village is right in front of the player.

https://drive.google.com/file/d/0B7AO0v4hK3VgZ1ZMRVh4OFdyckE/view?usp=sharing