How can I stop a toilet seat from rapidly loosening?
Nylon is self-lubricating. Even when tight it's very slippery against itself. You'll need to increase friction. 

It may seem counter-intuitive, but you could apply some PTFE (Teflon) plumbing tape to the bolt threads. Even though PTFE is used as a lubricant, it'll thicken the thread diameter and create resistance to movement. Wrap 3-5 layers on the threads where the nut will rest, in the direction the nut tightens (clockwise from the end of the bolt). 

You could also replace the nuts with brass or aluminum. They'll grab the bolt more aggressively. Be sure to use soft washers against the porcelain surface to prevent damage.

One other thing that can help is to reduce slide movement of the seat on the bowl. Install rubber washers under the seat bolts to create some grip.