It is highly unlikely to be Inner Space causing it, as Inner Space does not install any kind of filter driver to your NIC. It does use your network like any other service, i.e. it will open a port back to the auth servers when you launch a game profile (or ISBoxer character set/slot), and then close it. If you happen to run multiPC then it will listen on the specific port (usually 10101), but this wont affect the other 65534 ports. Besides for that kind of issue, it should be more than just you experiencing it.
The most likely breakdown of internet services like this is some else which is preventing your NIC filter drivers (e.g. the TCP driver, QOS Schedular) from working, or another filter driver which happens to be running or even the most likely, some kind of Internet Security program.
I have had services which exhibited similar behaviour where they stopped new connections, but serviced anything existing, which sadly turned out to be something completely unrelated to the symptoms, where the network traffic was failing to buffer due to an inability to write to disk, due to incorrect configuration of the disk. Just showed me that sometimes it is not what you think.
I think your best course of action at this point would be to get a
Diagnostic for crashes (yep, I know it is not crashing) on the InnerSpace.exe process (yes, I know I said it wasn't likely to be Inner Space too, but this will show us if anything is hooking it).
Also, it is probably worth noting that Inner Space and mumble and discord's overlay systems may not play nicely with Inner Space/ISBoxer and it is recommended to disable them while multiboxing. This applies to a few
other notable software items.
p.s. I also get a similar problem on my setup at home on the wireless. I switched to wired connection to make it go away. BT have yet to acknowledge it, but from my testing, once I push about 4GB through the HomeHub5, it falls over until I reboot it or my computer (basically I need to drop and reset the connection between my PC and the router).