I give up.
I've added three similar products to my shop today, all of which have the same variants (ie the user has to select a single variant - confirming that they are old enough to purchase the product). The first two were copies of another product and all went well. The third product was another duplicate, but that refused (6 times) to select any variants. So I started afresh. Same problem. 5 attempts.
Just to confirm; you can give it attributes and save the item, but when you go to select the actual variants (so that you can give them a price and quantity, etc), absolutely nothing happens.
Cheesed off & seriously considering pulling out of WooCommerce.