You can make a fine recording. Assuming you're running a stand, get a good light stand umbrella to protect your mics, and trash bags and a waterproof gear bag to protect your rig (put the rig inside the trash bag so it doesn't get wet from the bottom).
Obviously, if the rain is actually hitting your mics, it's up to you whether to keep going. I put heavy windscreens on, but if my screens were getting more than the occasional drop of water, I'd pull my rig down depending what rig I was running.
I've even made one good pull where I had stealth mics on a hat and had to throw a couple of shirts over my head and make a makeshift hood around my head.... and it was POURING that day.