We investigate effects of the electron traps on adiabatic charge transport in graphene nanoribbons under a longitudinal surface acoustic wave (SAW) potential. Due to the weak SAW potential and strong transverse confinement of nanoribbons, minibands of sliding tunnel-coupled quantum dots are formed. Therefore, as the chemical potential passes through minigaps, quantized adiabatic charge transport is expected to occur. We analyze the condition for a closed minigap, thereby destroying the current quantization in a nanoribbon. We present numerical calculations showing the localized energy states within minigaps. Additionally, we compare the results with the minibands of corrugated nanoribbons.