I have a no4 mkI enfield (see before and after pics) and it has a tasco pronghorn 4X32 (upgrading soon). I have had no problems with losing zero. Also I have a side mount (reciever needs to be drilled and tapped type) scope mount I got from brownells years ago, but ATI (same ones that made my stock) make a no gunsmithing mount.
The scope is great and can be picked up in different confingurations (3-9X40, etc.) for dirt cheap since they discountinued the line (check ebay for some new discontinued stock under 40 bucks).
before enfield no4 mkI owner before me roughly sporterized
After: nice sporter! reparked, new spring for bolt, new ATI stock (from brownells), barrel shortened to carbine length, fiber optic sight installed on front blade sight.