Conditional commandblocks act differently to a change in direction than non-conditional. This is apparently caused by commandblocks checking the block BEHIND them. Chain continues again when a non-conditional commandblock has been placed.
Regular commandblocks however do continue functioning after a change in direction.
Has been submitted before a long time ago and been marked as works as intended. Thought I would submit it again since I am not the only one thinking this is a bug.
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A non-conditional one doesn't need to know which command block came before it in the chain, and has no relevancy as to why a conditional command block can't get that information.
Consider the following setup: http://i.imgur.com/KorWP1K.png
Command blocks use the "scheduled ticks" mechanism to schedule the command blocks to execute in the tick after activation. That conditional Chain block has no idea which of the two chains activated it, so that cannot be used to determine which block to look at.
Keep in mind that Impulse and Repeating blocks can also be conditional, despite not have anything earlier in the chain to look for.
Duplicate of MC-93200. Please do not create duplicates on purpose. As you already said, this is considered working as intended, probably because of technical reasons. The conditional command block has no way of knowing which command block came before it in the chain, so it always checks for the one on its back.