I was having the exact same issue with my 380 EZ Shield the day I unboxed it. I verified that it was not my grip or trigger pull by having two experts fire the gun and they verified my findings. I sent it back to S&W and they sent it back to me with a new barrel. It worked better but it's still about 3" low at 5 yards. It's not like I'll be competing with it, but I would like some confidence that I could make a head shot from 10-12 yards.
I'm going to call S&W again to find out if there's a chance that their front sight might be a little too high.
I see that people are suggesting that an adjustment to the rear sight may be necessary, but according to the Owners Manual, adjusting for elevation is not possible on this gun:
The rear sight (FIGURE 89) is
adjustable for windage only.
Windage is the side to side adjustment
of where your bullet hits in
relation to where you are aiming.
To adjust, move the rear sight in the
direction you wish the group to
move on the target. For example, if
the group should move to the right,
move the rear sight to the right.
The word "elevation" does not appear anywhere in the manual, nor does any reference to the front sight being adjustable. I think I'll need to send it back to S&W again.