[A_Brandybuck]

There is a little reference to Durin VII concerning the Battle of Five Armies. YOu can find it in HoME XII: Peoples of Middle-Earth: Late Writings, Of Glorfindel, Cirdan and other matters:
The context of the mention is the reincarnation of the Seven Fathers of Dwarves in descendants of them.

In the Third Age Durin VI was slain by a Balrog in 1980. It was prophesied (by the Dwarves), when Dain Ironfoot took kingship in Third Age 2941 (after the Battle of Five Armies), that in his direct line there would one day appear a Durin VII - but he would be the last.

This fact sadly didn't make it to come into the Appendix. ;-)

For me the prophecy of Dain indicates, that the Time of the Dwarves comes to an end similar to the time of Middle-Earth. There was always a Durin (or came back after a time), the next should be the last. It doesn't sound good for the Dwarves. They have already been a dwindling race at the end of the Third Age.