Put a tarp or some other shelter over the fire, then the rain won't bother it and wood that you put around it to dry will actually get dry.
Obviously the tarp needs to be high enough that it doesn't catch fire. That means that to shelter the fire effectively if there's a lot of wind and little or no shelter from the wind, it will need to be reasonably big. A second tarp could shelter both you and the fire from sideways-driving wnd and rain.
I've used just a sheet of plythene, a few bits of cordage and a very big rock to make it possible to light a fire and keep it going realtively easily in very heavy rain.