What helps me with this problem with the R7000 is to remove the WAN cable from your cable modem from the back of your router for about 10 or 15 seconds, and then plug it back in. The router then regains its internet connection.
Not a great work-around, but it works for me in exactly the same situation. Takes a lot less time than 3 reboots, too *smile*.
I've reported this to Netgear for the R7000, and they've responded that they hope to have this fixed in their next firmware version. I hope so, too *smile*.
You should report this to Netgear for the R6250, as well. The more reports, the better. Just use the online Netgear Support issue reporting facility. You don't want to waste time on the phone with them.
Oh yes, one thing to add...you might keep an eye on this dd-wrt thread, if third-party firmware interests you:
http://www.dd-wrt.com/phpBB2/viewtopic.php?t=177443&postdays=0&postorder=asc&start=0
The OP of the above thread seems to want to add R6250 support in the future, assuming that he gets a development unit to use at some point.