They take a boat load of force, especially if it is the first time the base plate has ever been taken off. You really need a Glock Armorer's Tool (3/32" punch). Push the punch in as far as you can, which will usually result in the base plate insert displacing and ending up between the box of the mag and the spring. This is good because it gets it out of your way so that you can insert your punch as far as you can. Then, place your thumb on the front of the magazine and begin applying firm and deliberate pressure on the base plate, pulling it toward the front of the magazine to slide it off.
You have to be really deliberate with doing this. Trying to be gentle will not work. Paper clips and pen tips won't even begin to work. The base plate was designed to be dropped several feet time after time and not come off The notch cut outs in the base plate have to get over the nodes on the bottom of the magazine box.
Good luck and keep us posted