|The AIOs (guessing size L) lists 12 oz, and a L Sandys liner adds 7 oz. While that is enough for most kids, it's not too unusual for people to use two absorbent liners at night, and that's with the OS (13 oz) and L Sandys (15 oz). So it's entirely possible if you have a heavy wetter that you simply need more absorbency.
That said, diapers do need to be washed several times before achieving good absorbency. The unbleached cotton probably needs a little more washing than the bleached, simply because the bleaching process removes more of the oils from the fabric. 3 or 4 washes is probably good, but it may take more to get to truly optimal absorbency.
Another thing to check, with any diaper, is that you don't have anything poking out from under the cover. Although you don't have a separate diaper with the AIO, I've read that it's possible for the insides to sneak out a bit, so after snapping it up you'll want to run your fingers lightly around the legs just to check and tuck in any escapee fabric.
The other culprit can be fabric creeping into the diaper from the outside. I haven't found this to be an issue, but have read that sometimes people have trouble with very snug-fitting jammies getting in, usually around the legs.