My 3880 has never asked for a self-cleaning, but it has clogged. I leave it on 24/7 but it gets a print every 3-4 days too and I keep a vinyl cover over it when not in use (Fwiw, I also have a Canon 9000 II (dye) and it has plugged as well.). Usually the PK or MK if I don't switch between them enough. I have had the dark magenta K3 plug too. Usually a nozzle check to verify, let it sit, and check maybe in another hour or two to see if it is still missing the checkerboard (I do it from the printer menu and not the computer.). If fail, then a full power cleaning and let it sit maybe overnight and try a nozzle check again the next day. Seems if I soak the head with ink, it takes a while to soften up the clog part and get it back working again.
The worst I have for plugging is a small Epson Charm (portable for field use) with a battery. Damn thing will plug badly in a week or two and then it takes 3-5 cleanings which leaves me with an empty $45 ink cart (Also dye ink I think?). I've sent back a couple of unused paper packs to Epson who reimburses me in 8 weeks (Ink and paper are packaged together for $45). Still, I wonder if Epson doesn't have their ink formula down pat at times if even their dye ink printers clog in short order?
I would guess letting it sit with a clog and no ink would be worse overall, but don't really know. Good luck.
SG