Technically they've always done some recording fairly soon (within weeks) after the end of the tour. They worked on Rattle and Hum tracks in the winter/spring of 88, for example; recorded Zooropa in the break between Zoo legs; and even went into the studio six weeks after PopMart in the hopes of having a new album out at the end of 99. It seems like this has been something they've done as a way to A) capitalize on the tight-knit nature of the band after so much time on tour, and B) expend some of that energy. The only times they haven't done this was after the LoveTown tour (the earliest evidence we have of any recording is Edge doing demos in his basement in spring of 90 with drum machines), after the ZooTV tour, and presumably after HTDAAB, when they seemed to take a long break, no doubt because of Edge's family situation, combined with the pressure from Spider Man to start writing material in earnest.
There was never going to be a new record in 06, since the tour would have only finished that spring. Once it was pushed to fall, it definitely wasn't going to happen. I'm guessing this was when they worked with Rubin, since wasn't the band in LA anyway because of Edge? They could have possibly released a new record in 07, had the Rubin material they were working on been up to snuff. But it sounds like they abandoned those songs quickly after 06 and started afresh with Eno/Lanois in spring/summer 07.