Is it safe to keep a step-down converter turned on at all times?
A step-down converter is generally just a transformer, though some might be autotransformers. An ideal transformer never consumes any power itself; it simply transfers power from its input to its output. If you leave an ideal transformer connected to a power source with nothing connected to its output, it will draw no power from the source. Real transformers are not quite ideal, though some of them are very close. A real transformer connected to a power source, with nothing connected to its output, will draw a small amount of power on its own and might warm up a little. Similarly, a small percentage of the power transferred from input to output by any real transformer will be lost (converted to heat). The difference between a transformer built to transfer 1000W safely to its output, and one built to transfer 750W, is that the 1000W unit will be engineered to dissipate more
