Yes, they typically are. The proper fix is to install gas port reducing bushings. They reduce the amount of gas used to cycle the action, and therefore the slamming back and forth, which is what breaks cheap scopes.
The real culprit is inertia: the scope tube wants to recoil with the rifle, while the scope's guts want to remain stationary. Given equal quality, a light, small-objective, fixed-power scope with its lower inertia and fewer moving parts will hold up to recoil better than a big, long heavy variable with a big objective and more internal moving parts.
I had a Simmons 2.5 x 20 on a Mini for a few years without problems, but it's a smaller scope than the 4 x 32. If you're extremely cash-restricted, you might want to try that. I'd seriously look at the Leupold Rifleman, Weaver K-series and Nikon ProStaff lines, however. A fixed 4x can be had for a little over $100. Conceptually, cheap (not necessarily inexpensive) optics don't really make sense: one good-quality scope costs less than 2 cheap ones.
If good glass is beyond your current budget, I'd stick with the factory aperture sights until I saved up enough. Going back to an iron-sighted Mini reminds you of just how much fun and useful a light, handy, well-balanced rifle can be. Since most Mini-14s are not tack-drivers in the accuracy department, a scope (especially a big, high-power one) doesn't really add that much, and it upsets the balance of the rifle, IMO. One of my Mini-14s is set up with a Williams aperture sight for just that reason. I grab it more often than the scoped one.