Got a weird problem here. On my Windows laptop, I get the above error whenever I try to do an online plate solve. The problem does not happen with KStars on my Linux computers. I tried 2.9.5 and 2.9.6.
So I figured I'd download the source and remove the networkAccessible() check, and let it try to online solve anyway, without checking if the network is accessible. Well, when I build KStars from source (took me a couple hours to figure out how on Windows), everything works! With no modification to the source code.
At first I thought it might be the different versions of Qt that we're using. I tried a simple test program with various versions of the Qt libraries, where all it does is check QNetworkManager if networkAccessible() and print the result. It works as expected with Qt 5.9.1 and 5.10.0. My builds are 64-bit, where it looks like your build is 32-bit, but that shouldn't make a difference (I think).
I'm stumped, but at least I have a working KStars now, and can start working on one of the things I wanted to work on, but never got around to because building KStars from source on Windows looked like too much of a pain.
Hold on, just discovered something. Just finished downloading and installing the Qt 5.10.1 libraries, which is the exact version of Qt that the official KStars is built with. And my little test command line program is broken! On 5.10.1, the return code of networkAccessible() is NotAccessible. On 5.10.0, it is Accessible.
A little more investigation reveals this only happens with WiFi. As soon as I plug in an Ethernet cable, it says network is accessible. Unplug it and go back to WiFi, and it says network not accessible.