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What would ZIP/ZIPPER mean in the following display messages (packaging equipment)

It's pretty hard to tell without knowing the equipment, or its components.
Normally a zip is a clothing zip: http://en.wikipedia.org/wiki/Zip_fastener
If it's packaging, and not clothes, it may be something like a ziploc-type zip. http://en.wikipedia.org/wiki/Zipper_storage_bag

Since you said that these display messages on packaging equipment I think that they would mean the following:

Zip punch delay and duration too long- The process for making a stop (zip punch) is delayed because the duration entered is too long.

Zipper end of the reel- The material used to make the closure has run out ( I am thinking the material you are using is on a reel)

Zipper frequency controller is not ready - The machine that you use to program the closure frequency is not ready to work.

I am not 100% sure of my answers because I don't know the exact machine you are working on, but I would say my answers can be used in programming a machine that would make some sort of closing process. It would be helpful if you said the name and model of the machine you are talking about. I hope this helps.