If it's not cycling the next round, there's (a) not enough recoil generated from the ammo, or (b) too much friction in the slide to allow it to operate.
Since you've cleaned and checked the gun, my guess is that the ammo is just too light to operate the pistol reliably in its current condition.
If you can make the ammo work, but your daughter can't, you know where the problem lies. If the gun has worked reliably previously with this ammo, then it's pretty much got to be dirty somewhere. Maybe a rigorous cleaning of the slide with gun spray, making sure that you clean the firing pin area, might help?
I've got this pistol and have never had a single function problem except when I tried to use under-powered ammunition.