OT, I'm far from being an expert. I worked at two on-campus radio stations in my first freshman year of college (that's part of the reason there was a second freshman year - I don't have a good excuse for the third freshman year), and although I was fairly good at it, when I tried to find a paying job in that oh-so-glamorous profession, I found that I could do a lot better working for a living. But it's still a fun thing to do, and I still pay a reasonable amount of attention.
I know nothing of beethoven.com's finances, and I'm not even going to ask, since it's none of my business. But most of the radio personalities I know have other jobs that actually pay the bills. When I lived on Los Angeles, there was an announcer (Rich Caparella) who worked the classical stations - First he was on KFAC, and when that folded he went "back" to KUSC. Then KGGO (now KMZT) went classical, and he went there. I also saw him on PBS regularly, and he announced at the Pacific Symphony concerts I attended. He did a lot of things besides being the morning man of LA classical radio, and I'm sure he was one of the better paid announcers.
So I have no idea if beethoven.com could afford another live body overnight. To be totally honest, I expect the station could run without live announcers, although they would lose a little of one of my favorite features - requests played within an hour or two. That pretty much requires a human, and I like the trio they have.
As I've noted, there are stations with virtually no live operators. A guy gets a license, a transmitter and antenna, and runs the whole thing from his basement or garage. Most of the time, he's just got a CD carousel playing random cuts from his collection. He sells a few ads to help make ends meet and pay his royalties, and has a nice hobby. This isn't all that unusual in smaller markets.
--I know what I like--