[UPDATE: It's taken a few extra months but I have a new theory. Read it below.]
A quick Google (from my phone - doh) identified that the problem may be a faulty device driver update, which I'm guessing my laptop helpfully did in the background. The solution, on Windows 7, is just this easy:
Start -> Control Panel -> Device Manager -> Network Adapters -> [Select your wifi adapter] -> Driver Tab -> Roll Back Driver.
One click of that, and everything works like an absolute charm again - no reboot or anything needed. Just in case you'd like a visual cue, it looks like this:
Thank you for fixing my Internuts, Internuts!
UPDATE: 23 July 2014.
I can't tell you how many times I'd updated my Windows software, rebooted, adjusted the power settings, and all the other tricks in the book, before finally stumbling across an all-new solution which really seems to work. I've been using an Android cellphone as a mobile wifi hotspot, and I'd started to suspect that it was the root of both my and my wife's laptops being kicked off the internet and then not letting them back-on. The solution is as weird as it is simple: just unplug the cellphone from the charger! Don't ask me why, but this results in perfectly stable wifi connections. Plug it in again, and bang ... symptoms immediately re-emerge. So it probably is some power-related issue (genius deduction there), but I don't think there's been a how-to written online that explains it. At least now there's a solution, and hopefully it helps you too.