Not under this proposal, as long as you continuously updated the software. If you never payed the tax, the version from two years ago would lapse into public domain, but any maintained versions would continue to be copyrighted (or at least contained copyrighted elements) as long as effort was expended to maintain them. In theory there is nothing preventing this from happening with GPL software now, except that the length of time for something to go into public domain is so long.

Edit: In some ways this is actually an improvement over the status quo. It solves the problem where software can't be relicensed because no one can track down all the authors. You only have to track down the authors who have been active in the last two years.