Why won't my pudding thicken up?
You are probably stirring the pudding too much. Cornstarch starts thickening at about 205°F/95°C. Once the pudding has got to that point and has thickened, stop stirring, otherwise you will interfere with the starch formation that causes the thickening. Using electric beaters probably means you are missing the point when the pudding has thickened and quickly beating the living daylights out of any starch formation that has occurred.

It may also be the case that you are beating so much air into the pudding that it just doesn't get hot enough to activate the cornstarch in the first place. I would use @ecnerwal's suggestion of a double boiler, along with a balloon whisk, and some patience.