It is shown that due to disorder the excitation gap in the fractionally quantized Hall effect is reduced and goes to zero at a critical magnetic field ${B}_{c}$. Impurity scattering defines a lower critical field ${B}_{c1}$ and surface roughness scattering an upper critical field ${B}_{c2}$. The observation of the fractionally quantized Hall effect is restricted to the magnetic field range ${B}_{c1}$${B}_{c2}$. We discuss the influence of finite-thickness effects of the two-dimensional electron gas and spacer-thickness effects on the lower critical field. We compare our theory with experimental results on the magnetic field dependence of the excitation gap at filling factors \ensuremath{\nu}=(1/3, (2/3, (2/5, and (3/5 in GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructures.