Battery Cable problems of the 2004 Mazda MAZDA3

Issue: all electrical components along with power steering shutting off intermittently while driving. The first instance of this issue happened while turning into a parking lot. As I was making a right turn all the electrical components in my vehicle shut off, along with the power steering. About a second later everything came back on and operating normally. This same issue would happen intermittently, usually when making right turns. There was never enough of a pattern to say that it was happening every week or month, etc. I took vehicle to Mazda dealership and they diagnosed it as battery cables needing to be replaced, after it started happening more frequently a few months later. The issue stopped for a couple months, but then began again. This time it started happening just by tapping on the brakes as well as making a turn. All the electrical on the vehicle would shut off, along with the power steering again; and then it would come back after a second being off. This time it began happening much more frequently, at least a couple of times a week; most recently it happened again and this time my power steering was off for my entire 30 mile drive home from work. I took it again to a different Mazda dealership to have it diagnosed, and this time I was told they needed to change the battery, alternator and power steering pump for starters; but was not guaranteed that would resolve the issue as the techs had never seen this issue before at their site; they say they called their corporate tech line and were advised to replace those items first. I even showed them a video I had taken of this happening in my car one night as I drove around my block in order to document the issue. There is no pattern with regards to speed of vehicle, or whether the engine is cold or has been running for a while, as the issue can happen regardless of any of these conditions.