Three-dimensional photonic crystals with fall bandgaps at optical wavelengths can be fabricated with inverse-opal techniques. We have shown that the bandgap is extremely sensitive to the presence of geometric disorder in the crystals (see Figure). The bandgap closes completely with a disorder strength as small as under two percent of the lattice constant. This fragility persists even at very high refractive index contrasts and is attributed to the creation of a bandgap at high frequency bands (8-9 bands) in inverse-opal crystals. This should impost severe demand on the quality of lattice uniformity.