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The printer will stop completely after a certain amount of prints (overflow), normally requiring you to take your printer to an Epson dealer for servicing and resetting.
The service maintenance that would then be carried out is the draining / replacement of the ink pad that catches all the waste ink and resetting of the protection counter.
The ink pad replacement may be unnecessary, as this is rarely full when the maintenance messages appear. Therefore, the only requirement now is to reset the counter which will then release your printer hardware and start counting your prints from zero once more.
If the printer has passed the maximum prints and you've continued printing throughout the warnings, after the 'overflow' amount of prints, it will lock out completely giving you two flashing lights on your printer which you can't reset without this software or without pressing a sequence of buttons.