There are probably more than a few Artisan 725s out there. I reckon that if this is an inherent problem with this printer we'd have a heard a lot about it by now.
I suggest your next step should be to print using the recommended ink and paper - some non-recommended materials can be very incompatible.
I've occasionally fed Epson Premium Luster paper the wrong side up, by mistake, and the result it weird - the print comes out still very wet, you can do some interesting things swirling it with your fingers, and it never sets/dries. I think the base is some kind of plastic or plasticised material, with an 'ink-receptive' coating on the face.
Even when fed correctly there is the occasional surprise, such as trying to write on the back with a ball-pen - that never dries either, which can be inconvenient. Most "write on anything, including glass", e.g. 'Sharpie', pens are OK.