The headspace for a 38 Special is .060, .066 max. or altrernatively, .006 case clearance. 38 Special rim thickness should be .048 min/.059 max.
On the opentop models, there is a gas ring. If you overtighten the wedge, the gas ring will get clamped between the frame and the barrel. Push in the wedge until the retaining screw can be rotated into the wedge's well, then push the wedge back outward against the screw's head. If there is little or no endshake, it's possible the headspace might be too tight.
The headspace should be set, when installing a new cylinder by adjusting the height of the rachet teeth. Once that is set, the length of the gas ring is adjusted to provide enough endshake to allow the cylinder to rotate with the wedge in the correct position. The Uberti factory presumably does that.
As others have suggested, check the retaining screws, the gate screw is a frequent offender, Locktite it.
Also check your brass against the dimensions I gave at the top. There is a difference between brands of brass, see if one of the makers (often Starline) is too thick.