@gfw 

I would test by making the 5G name different. Even if a device is only capable of 2.4G something may be happening related to that. 

Other things you can try is to modify the version or encryption in the wireless settings of the router then seeing if the devices are able to connect. (Advanced > Wireless > Wireless Settings). 

@Tony Thanks for the reply. Separating 2.4GHz and 5GHz SSIDs has made no difference, but I'll try changing some other details and see if anything helps.

@gfw Can now confirm:

Restarting the router and the devices with separate 2.4GHz and 5GHz SSIDs temporarily gives all devices access to the network.

Changing settings makes no difference.

I refuse to reboot the router and every device attached to it every ~2-3 days, and one of the devices affected is my thermostat so I can't just ignore it in mid-winter. I'm going for a different router from a different manufacturer, and I'll be seeing if I can offload this janky piece of kit on eBay or wherever.

@gfw 

I agree you should not have to reboot every few days.

One thing that we see is when a new router is installed and especially with the same SSID and password, devices may not connect or have other connection issues. On the device that has the issue, deleting (forget) the network and re-establishing it clears the issue. Also be sure you are using the power adapter that came with the router.