My best guess would be that the ink switching unit is starting to fail. It is the part that switches to and from MK and PK and can exhibit this problem before total failure. When it does fail, it is usually stuck with the PK permanently draining, and becomes only usable for printing MK.
One diagnostic is to weigh the PK cartridge to see if it contains as much ink as the system claims. I have a 3880 where the PK weighs empty, but shows 81% full on the printer's front console screen.
Epson estimates the lifespan of the 3880 at 5 years, and the ink switching unit is a known first point of failure.