Can I take up and reuse clickable floors once the've been put down?

I have this guy putting down a floating wood floor. He's not done yet, but we've already noticed that it is seriosly squishy in the hallway. I know the reason. When I did the prepwork, I found that there was a different kind of subfloor in the hallyway and there was some black rubber stuff over it. It was a real pain to remove, so I talked about it with the contractor and he said that as a matter of height difference, it was probably doable. There is a somewhat noticeable difference in the level when you walk into the hallway, but it's not a huge deal. The real problem is that it is seriously squishy there. In contrast to the living room, it feels like you are walking on a cushion and you can see the wood depressing as someone walks across it. I really don't feel like putting any more money toward this right now. I wish the contractor had told me it might be like that if we didn't remove all that black stuff. I'm wondering what options I might have. Has anyone ever taken clickable floors up? Can I put it back down after I take it up? Or will it be better if, after I put the base board back on, I put it on good and tight?