Well... depends on what you're doing. I've known quite a few "robot programmers" who were excellent at hands-on motion path programming, and could squeeze every last millisecond out of a complex motion in tight quarters... but had no "programming" skills in the sense of writing software.
My opinion is that this type of job is dying out, however -- the industry is moving away from "hands on" programming towards "offline" programming -- complex robotic operations programmed and debugged entirely in virtual environments, with little to no hands-on work performed in the actual deployment.
One exception to this may be "cobots", which are designed to work alongside human operators and to be "trained" by unskilled operators.
So, skills. At minimum: Basic skills in general programming, at minimum -- the ability to look at a program and grasp what it's doing, and make modifications to it. Electrical and mechanical troubleshooting skills, enough to identify faults and repair minor breakdowns. A sense of the robot's kinematics -- how it moves, what moves work well and which ones to avoid (singularities, for example), and how the "logical" parts of the programs interact with the "motion" parts. A decent basic grasp of general computer skills, like installing and using different software packages, and how to connect a computer to other computers (or PLCs, robots, etc), including basic network troubleshooting. An ability to read manuals and documentation, locate the exact sections you need for a particular task, and figure out what the writers of the documentation failed to write down "because it's so obvious!"