Both twixt and its variant 'twixt show up a bit over at Google Books (link). Another set phrase it shows up in is the proverb: There's many a slip, twixt the cup and the lip. It sounds no more archaic to me than albeit or whom.
It sounds no more archaic to me than albeit or whom
Really? Wow. I use whom and albeit all the time, but I can't say I've ever used twixt.
The OED says it's an aphetic form of atwixt (which I've not heard of) and betwixt. They also cite an 1878 medical quote, which I found interesting: "These primitive cerebral vesicles give rise to new segments... The first is known as the Fore-brain or Prosencephalon; the next as the Twixt-brain or Thalamencephalon." I've not heard it used that way.