Radiation can affect the electronics themselves (by corrupting data, or by slow physical degradation of the physical hardware) but other than that, I don't think it has any particularly noticeable effect on communications.
The "radiation" from a reactor core mostly consists of highly energetic particles and gamma rays. It's not going to directly interfere with anything in the radio spectrum, or induce significant voltages on cables.
I'd think it's much less of a concern than in space. For one, space robots are far enough away that there's a big time delay to Earth communications, these robots will have control stations <1km away. So the only electronics on board the actual robot should be fairly rugged motor drivers and wireless comms. Add in an extra redundant copy or two of all the IC's (and possibly enough motors to give redundant degrees of freedom), and a policy of pulling out and rebuilding the robot when a certain number of non-function-impairing radiation damage events occur, and it's a non-issue.
Radiation causes huge headaches in space because there's no way to pull it out or send in a replacement, and comms have seconds - minutes of lag. These don't apply to Earth based robots, even in super hazardous environments like this.
Also they won't need to lift the robot's mass into space (which costs on the order of $5000/kg), so for most of the 'bots, they will be able to easily add additional shielding around critical electronics. Robots which are intended to fit into very small spaces might not have this option, but also hopefully will be cheaper than their larger brothers.
I wonder how many robots will become part of the contaminated decommissioning waste. Perhaps they will develop robots to disassemble and store the damaged and contaminated robots, filling a function like decomposers in nature.
I'm assuming that these are 'built to last' - as once they are no longer working I can only think that they themselves would become radioactive waste that will need disposing of.
Is it unlikely that a human would be able to work on the robots to repair them due to the levels of radiation?
As far as possible, you don't put complex electronics in there. Motors connected by an umbilical cable to the operator, analogue sensors, etc. In some situations you might be able to use a mechanical or hydraulic system.
"Most nuclear robots operate on power provided by a trailing umbilical. This means there are no batteries to change and no refuelling issues to contend with."
It's reasonably rare to have full or even semi-autonomous in nuclear due to the risks involved of something going wrong, or the thing just dying. Easier just to remote control down a cable.
Yes, it would have been nice to have more information on that since this is a serious problem. Shielding helps up to a point, but you need a lot of shielding to keep out gamma radiation and hot neutrons.
