There are two common issues that will cause this to happen. The one I see the most on the older Mimakis is the "ink end" sensor is damaged and/or out of alignment which is causing the machine to think the cartridge is empty when it isn't. Take all of your cartridges out and look in the cartridge holder with a flashlight. The sensor I am talking about is towards the back, bottom right side of the holder. It is a black plastic lever that should be sticking out very slightly from it's housing. Compare each of the cartridge holders and see if any look like the lever is broken off, sticking out too far or damages in any other way. It's a very sensitive sensor so if it is damaged at all, it will always say your ink is near end.
The other reason the machine would mark the ink as empty when it's not is the maintenance station is failing. This is more common on Mutohs but can also happen on Mimaki machines. Normally you will notice that cleaning cycles don't recover nozzles like they used to or it takes more than one cleaning to get all of the nozzles firing. This is a good sign the maintenance station is failing and you should replace at least the cap top especially if it has been more than a year since the last one. What happens is the machine guesses at how much ink has come out of the cartridge when a cleaning cycle or print job is run. It has no idea how much ink actually was taken out of the cartridges which means that if the maintenance station isn't pulling as much ink as the system thinks it is, you end up with a cartridge full of ink that the machine thinks is empty.
Find a 3rd party ink supplier who can get you ink chips to put on the other cartridges. That way you can use the ink that is still left in the cartridges.
Edit: Once a cartridge is marked as empty, it is empty even if you fix the issue that caused it. I wasn't sure if I made that clear or not. That is why you need new chips.