DIAGNOSIS Spilled liquid or sticky residue has seeped under the rubberized button pad and is gumming up the micro-switch underneath.
FIX Unplug the unit. You can't easily remove the button pad, so you need to clean around it. Dampen a cotton swab with a tiny amount of isopropyl alcohol (rubbing alcohol). Wring it out so it's just damp, not dripping. Gently work the swab around the edges of the Pulse button, pressing the button repeatedly as you clean to work the alcohol in. Follow with a swab dampened with just water to rinse, then dry thoroughly with a paper towel. Let it sit for an hour before plugging back in.
IF THAT DIDN'T WORK If the button is physically stuck down, something might be lodged underneath. You'd need to open the base housing, which voids the warranty. If it's under warranty, contact Cuisinart. If not, and you're comfortable, you can find teardown guides online to access and clean the switch directly.
HEADS UP Never pour or spray cleaning liquids directly onto the control panel. Always apply cleaner to your cloth or swab first. The seals around those buttons aren't waterproof.