There seems to be a bug in regards to whenever a skeleton shoots an arrow and you have your shield out. It will bounce back, but it won't damage it. The arrow just goes through it.
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This issue actually appears to be a duplicate of MC-147233, which hasn't yet been resolved. If you have any additional information to provide regarding this issue, feel free to comment on the parent ticket. If you feel that this issue is affecting you, feel free to vote for the duplicated ticket, to give Mojang a basic idea of how many people are impacted by the problem. Just to further inform you, this will not determine how quickly the bug gets handled or fixed.
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Please provide a screenshot of your game with the F3 debug screen enabled.