@Psker
I fear there is no way around it. Robots.txt is basically a command implemented in sites whose owners don’t want that their site gets archived on the WaybackMachine. If the WaybackMachine detects that on a site, it doesn’t archive it.
I don’t know why it’s there on the cached site of a Tumblr blog while cached content of other sites works without issues, but that’s how it stands.
There is one other blog you can archive. It’s not in Google Cache, but furrypony said it should be archived on the WaybackMachine because of its beautiful design and he’s right, there was a lot of effort put into that design.
Plus, it’s a blog by some of the biggest creators in the fandom, Silly Filly Studios, so it deserves a bit of extra archiving. Also because of the memorable posts they made over the years, which might not be able to be recovered with TumblThree. You can find the blog here:
http://sfs-animation.tumblr.com/
The arrows to click through the individual pages are under the SFS logo on the left side.