I have a Brother HL-3140CW. It seems to be a decent network printer. Unfortunately, one day it just... stopped. I tried the wifi setup and it refused to see my SSID (or any other for that matter). I tried WPS to no avail.
In my case, it turns out that my router (a piece of junk supplied as stock from Virgin media, because I'm too lazy to swap it out) was using channel 1 for our 2.4Ghz network. So was nearly every other network in the building (about 18 of them). Switching to a less congested channel seemed to do the trick.
If you're not sure if you're on a congested channel, try a tool like wifi analyzer (https://staging.f-droid.org/search?q=wifi+analyzer) - or search on the Play Store if you prefer and it should get you started.
Note - at some point I had the printer set up so it was broadcasting its own SSID - "SETUP". You'll need to disable that (in the printer's network settings) to proceed.