No. Not "Since a long while" -- "FOR a long while."
But I suppose it doesn't matter. That is to say, it matters to me. "Since a long while" bothers me -- but it shouldn't, according to whose principles? Mine. I'm the one who's always opposing those who insist upon one standard English spelling which, they claim, is "correct."
I'm the wun hoo spelz thingz "rong" on purpose just to annoy those people who insist on "correct" spelling. I'm the one who's constantly insisting that they're missing the whole point of language, which is to communicate, and that we all know exactly what was meant however it was spelled. Do we all know exactly what the non-native speaker of English meant when he said, "Since a long while"? Yes.
It has never bothered me that, when Latin became an international language, a second language spoken by people with many different first languages, it changed quite a lot, so that the international version often sounded quite strange to someone born and raised in Rome whose native language was Latin, or to someone today who insists that the Latin written by Caesar and Cicero and Vergil and Livy is "correct" Latin, the only "correct" Latin. Medieval, international Latin bothers some of those people quite a lot.
I suppose it must be very much the same sort of deal when adherents of Classic Attic Greek become appalled by the international Koine version. Or when Castilian purists from Spain insist that Latin American Spanish is wrong.
And exactly the same thing is happening to English today: more and more people are speaking it and writing it as a second language and forming an international version of English which may often sound somewhat strange to a native English speaker.
It's not all that different from the way that we Americans and the British and the Australians have all sounded odd to each other for centuries now. Not to mention various Canadians, Scots, Irish, Welsh and New Zealanders.
I've always laughed at those British folks who took their own arbitrary habits so seriously that they actually became angry at how Americans speak English. And here I've caught myself do the same thing I've laughed at. It IS "since a long while" now in addition to "for a long while," you know why? Because language is much too big and powerful and moves and changes much too fast to have any reason to stop and ask for my opinion about how it's doing.