This sounds like Blackleg which is unfortunately a common problem with Pelargonium cuttings. It’s caused by a micro-organism which is spread by using unwashed pots/trays or tools. Using water from a source other than mains water can also cause this.
The only way to prevent it is to sterilise everything the cuttings will come into contact with - pots, trays, secateurs etc. Make sure you use sterilised compost from your local garden centre and it wouldn’t hurt to dip the cuttings in a rooting hormone which contains a fungicide too. Make sure the soil isn’t too moist as the disease will thrive in these conditions.
Dispose the affected cuttings with normal household waste to prevent it spreading.