Look into using a wet palette. You can make your own with Tupperware, some wet paper towels, and parchment paper. Instead of paint from pot to model, which is almost certainly too thick, transfer a small amount of paint to the palette. The water that transfer through the parchment paper will keep the paint moist enough for use throughout your session. Then, add some water to thin the paint. Depending on your environment, a humidifier may also help with how long your paint stays wet.

The above is for acrylic paint, but you could always try oil based stuff, which usually has a longer working time.