The seat on my toilet always works itself loose. It has plastic thumb-screw-style nuts that tighten on to bolts on the underside of the toilet. The left nut works itself loose over the course of a few days of normal use. I can tighten it again but a few days later, the seat is back to wiggling around from the loose connection.
How do I get this arrangement to stay tight?
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.
It is likely that the plastic nut (or bolt it screws to) is stripped. It may feel like it is tightening, but works loose because the threads are damaged. You should grab a set of replacement toilet seat bolts at the plumbing shop, they are (fairly) universal and come in a set of two. You do need to tighten rather firmly, but it is easy to damage plastic threads by overtightening.
Buy a set of new bolts and replace the bad set.
The one that loosens is stripped or contaminated or manufactured poorly.
Make sure everything is squeaky clean before reinstalling the seat with the new bolts.
If nothing is damaged, get a second nut of the same thread (not necessarily a wingnut). Tighten the existing nut, then while holding that, tighten the second against it until they jam together. This works well with nylon nuts, but use too much force and you'll strip the thread.
I bought a set of Tank to bowl bolts with steel & rubber washers. Came with 3 hex nuts and 3 wing nuts. I put the hex nuts on first then double nutted them with the wing nuts. Working well. Previous nylon bolt had snapped off.
Duct tape wrapping it all or the tightest possible after the bolt on the free part of the thread.
