On cheap cameras, the IR is often a separate “dumb” circuit that just turns on and off with light levels. So seeing IR does’t always mean there is enough power left to run the camera electronics.
I’m assuming that the video baluns are being used for particularly long runs. Long runs introduce more resistance and when load increases (IR) the voltage can drop too low to sustain the camera.
You can try to cheat it a little and increase the voltage at the source a small amount to compensate with something like this or this but don’t cheat it up too much (~10%) or bad things will be more likly to happen (flames, fried camera, etc.)
It’s also possible (though less likely) this is happening on the regular cables. I used to evaluate and import cables like that, and you’d be shocked (ha) at the tolerance variations. Some cables are just better constructed and allow more current flow. IOW it might just be dodgy cables. (also try different male plugs on the cable splitter at the power supply for the same reasons)
Regardless, I’m 95% sure that the voltage is the issue here. Test this by covering the camera and seeing if it dies, or shining a flashlight at it at night and seeing if it comes to life.
The most common alternativs are powering the camera from a power source near the camera and using the cabling only for video, or using 24VAC with a 12VDC rectifier at the end, or pulling higher gauge power cable to the affected cameras.