Diagnosis
The rubber O-ring seal on the bottom stem of the water reservoir has likely gotten dislodged, dried out, or has a bit of mineral scale on it, breaking the watertight seal.
How to Fix It
1) Remove the reservoir. 2) Look at the black rubber ring near the tip of the plastic stem that plugs into the base. Gently work it off with your fingernail. 3) Soak the O-ring in white vinegar for 10 minutes to dissolve any hard water scale, then rinse it. 4) Make sure the groove it sits in on the stem is clean and dry. 5) Stretch the O-ring back into its groove evenly so it sits flush. 6) When you push the reservoir back onto the base, press down firmly until you feel and hear a distinct click. That click is the seal engaging.
If That Didn't Work
Inspect the plastic stem on the reservoir for any hairline cracks. Also, check the black rubber gasket inside the hole on the base where the stem inserts. If that's missing or torn, you'll get a leak.
Heads Up
Never force the reservoir on or twist it. Push it straight down. Twisting can pinch and cut that O-ring. Use distilled or filtered water to slow down scale buildup on all the internal seals.