That's really weird that there is new firmware on the website, but when I press the button to check for new firmware in the administrator for my DIR-645, it said that the firmware was up to date at 1.01. Bug?
I updated the new 1.04 firmware (the 1.06 you mentioned was noted in the title of a security advisement here: http://support.dlink.com/ProductInfo.aspx?m=DIR-645), and I also added the 1.04.B13 security patch. Now when I press the 'Check Now' button to see if the firmware is up to date, I get a message that says 'no response, make sure you're connected to the internet'. There is no doubt that I am connected properly to the internet.
Anyway, the 1.04 firmware update on the router hasn't made a difference, I still get 'Cannot connect to camera' on both local and remote.
Something else I tried was connecting directly to the wifi network of the camera from my laptop, then going to the admin by 10.255.255.1 and upgrading the firmware again, in case there was some issue with upgrading it while connected through my router. It did the same thing I mentioned in my original post, where the iframe changes to "The connection was reset" in the middle of uploading it. I had to power cycle the camera to get it responsive again. Firmware is 1.03.03, still get 'cannot connect to camera'.
Something I noticed is that on the support site for DCS-2630L (http://support.dlink.com/ProductInfo.aspx?m=DCS-2630L) firmware 1.03.03 is no longer available. Is there a reason for that? EDIT: looks like it's on the mydlink.com support site, but not the support.dlink.com site.