Do you do that part of the setup with the headset on? The Touch controllers communicate through the HMD, so if you don't have it on you, maybe you're too far away from it for the trigger to register? (Just a guess.)
You could do the Standing-Room-Only setup in Steam, and just rely on the Oculus Guardian walls instead of Chaperone (which is what I've done).
I guess the downside is that I think some games configure your play space based on the Chaperone area, so you might end up playing in a smaller zone in games like Job Simulator.
I was stumped by that too, but then I remembered the little detail about the Touch controllers wirelessly interfacing through the Rift HMD and thought "What if the Rift drops the Touch connection when in standby mode?"
Sure enough, I put my finger over the proximity sensor inside the HMD so it thinks I'm wearing it, and the Touch controllers will work as intended with the trigger.
It's a weird bug, considering that everything else works just fine without having to do that, but at least there's a workaround.
Still, given that certain SteamVR games do adapt themselves based on your available play space (Hover Junkers gives you a bigger ship if you do, for instance), it would be advisable to make sure the SteamVR settings reflect that.
I was having this issue too! Dumbfounding me because it's worked many times before. Thanks to everyone who knew the solution. Just engage that proximity sensor, and the Steam "Trace your Room" trigger works again.