I disassembled both the old and the new oil extractors this weekend, so I could see what happened to the old one. The old one has a "stop" of some sort in the center tube that had gotten sucked upwards in the tube during the last use. That's what was stopping the handle from going all the way down. I used a long metal pipe and a hammer to push it back down into the tube so the pump handle will again go all the way down. As odds would have it, the new one has a different center tube design and does not have the "stop" in the tube. I have no idea if I repositioned the "stop" correctly in the old one. If the old one doesn't work the next time I use it, into the trash it goes.
When the new extractor inevitably dies, I'm going back to doing oil changes the old fashioned way.