Some time back I put a $35 "el cheapo" red dot sight on my 14" Contender .45-70, which I would think has a tad more recoil than a .44Mag handi-rifle.
So far, it has held up to couple hundred rounds.
The trick to getting a good scope cheap is to find an older, quality scope, but not one someone thinks is a collector's item.
I am partial to the old steel Weaver scopes, (including the store brands), and I look for the low power ones with the POST /crosswire reticle. For me, nothing is faster in the woods. Easier to pick up than thin crosshairs when the background is cluttered. Just like looking at a front sight. Put the tip of the post where you want the bullet to go, and shoot.
Strangely not a popular reticle in sporting scopes today, but do note one (or more) of the very popular "tactical" sights essentially uses a POST reticle.
Newer scopes, with better optics, & coatings can give you better light transmission, and other things, but you are going to pay $$$ for that. Its up to you to decide IF the difference in performance is #1) something you can see and use, and #2) if it is worth the difference in cost, to YOU.