What to Do if your Pump "Sticks"
Do you not use the foamer regularly? As the pump is used, there is residual liquid on the screen. If the pump is not used frequently, that soap liquid can dry, creating a film on the screen which can ultimately clog the screen making the pump hard to use. Try using the foamer more frequently.
Is there liquid in the air chamber? You should see it inside the chamber below the pump. If so, turn it upside down and pump a few times which should get the water out of the air chamber.
Has there been liquid in the air chamber for a while? If so, clean as above. However, if the soap has had time to degrade the silicone in the pump, it may not regain the original amount of "spring".
Is the screen clogged? Remove the foamer and place the straw in some warm water. Pump water through (the water won't foam). If the pump is clogged with dried soap, then use the pump more frequently, keeping the screen cleaned.
Is the soap too thick? To work in the foam pump bottles the liquid should be water-thin. If it is too thick, the pump won't work properly and/or can be permanently damaged. To resolve, add just a tiny amount of water. If you dilute the soap too much, it won't foam well.
If the pump is still sticking and none of the above steps have resolved it, it could be the screen is not cleaning or the lubricant on the pump is dissolved. If you feel brave, try taking the whole mechanism apart and cleaning it with hot water. It may make it work again or it may remove all the remaining lubricant completely, causing the pump to become very hard to use - so don't do this unless you try all the other steps first.