You only clean it once a week. Rea Ann recommends you pour cleanser on your sponge after every use, meaning every day. Make sure to keep the plastic cylinder it comes in as a drying station.
You're scrubbing it too hard. Your BeautyBlender can tear if you have supersharp nails or if you're pulling the ends too hard when you clean the sponge. Instead, use a gentle squeezing motion. While the sponge is soaking wet, pour the cleaner directly on any soiled spots. Use a pinching motion to distribute the cleanser in and out of the sponge. You can also roll the sponge between your palms. And no, you can't put them in the washing machine.
You're not soaking it. For stubborn stains, you can also use a concoction of cleanser and water to soak your sponges overnight. If the spot still won't lift, you can pretreat your tool with a thinner oil (like baby oil) before cleansing.