We haven't seen the grid on the hull really get destroyed, either. When shields fail, there may be a couple of holes in the hull, or (before the age of CGI made showing of damage so much cheaper) no visible marks on the grid at all. Rather, some component within the ship has apparently failed.
For all we know, then, the same grid might be fired up by various pieces of machinery: combat shields might go down when their generator overloads, but another generator of (presumably) better power economy but lesser power can still be hooked on and provide "navigational deflection".
Timo Saloniemi