Reading the work of my younger academic colleagues, I get the feeling that whilst is making a comeback. Why would that be the case?
Strangely though, I don’t see this perceived increased frequency reflected in usage as we can access it through the Google ngram interface (I checked it for British English), nor does the OED record any instances more recent than those that are over a century old. So what is going on here?
Bridging the Unbridgeable 
Interesting question! I’m a (not younger) user of ‘whilst’, but in my corpus of c12million words of International Academic English (2006–2016), the ratio of ‘while:whilst’ is 7364:443. So no.
Well, you won’t know if you don’t break down the figures chronologically! Usage might be increasing. I for one now no longer correct a ‘whilst’ in texts I’m reading and revising into ‘while’. :-)
My personal impression (completely non-scientific and anecdotal, I hasten to add) is that -st words in general are on the way out. Words like amongst, amidst and (yes) whilst. I would definitely classify these endings as old-fashioned.
So would I, but why do young academics seem to use whilst more?
A form of hypercorrection, perhaps?
Possibly!
In the last several years I’ve started noticing “whilst” and “amongst” in the informal writing (emails, social media posts, etc.) of some of my under-40 friends and acquaintances. I don’t think I’ve heard any of these people say them out loud, though, so it may just be an affectation in writing.
Of course, it’s hard to say anything definitive without real data.
A really interesting thought! A few years ago, double comparatives and superlatives were also to be found on the social media. Deliberate and stylised hypercorrection perhaps, to follow up on Tony Parr’s suggestion? And you’re right, proper research is definitely called for!
I no longer tend to use it myself (though I’m ‘bobbing on’ in years) and, certainly, I assume its usage is going the way of ‘amongst’ and ‘amidst’ along with other words such as ‘twice’ (‘thrice’ having long since faded into history). If I were to hazard a guess, I too would posit that younger adopters are motivated by the desire to show off their command of a more ‘traditional’ style of written English. Interestingly, I noticed the use of ‘whilst’ only the other day on TV (though I didn’t make a point of noting the context), which is what attracted me to this posting. I do recall, though, that the word was spoken not written.
Quite by chance, I have just been speaking to a gentleman on the phone who works for the local municipal authority and he actually used ‘whilst’ while speaking. I asked his age and he told me 34. If I have contact with him again, I might enquire as to why he prefers this form. Watch this space, as they say!
How very interesting! Looking forward to hearing more.