This is a very strange bug and I have no idea why it happens.
Sometimes Dispensers and Droppers only fire when they receive a Block Update.
The Setup shown in the picture worked every time I built it.
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The dispenser on the bottom updated before all its power inputs turned off. It didn't update after that because of MC-108.

when you press the button it fires one time, but when you press it again it doesn't, so this is another bug. Also the dispenser is directly powered.