Yes, I had the cheap chinese scope on my first rifle, a Ruger m77 mkII fail in it's second hunting season. Missed the first two deer I shot at, after the second one thougt "that can't be me" and sure enough....the zero was moving all over the place.
I'm not sure what kind of scope you are dealing with, but that was a roughly $50 scope of indeterminate make that was all I could afford at the age of 17 after splurging on a rifle.
I upgraded to a Bushnell Elite for less than $300 and it served me until I sold that rifle actually, and I've rarely spent less than $400 on a scope since.
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