Hmmm.... it really sounds like a connection problem between the chip and sensor, because in my experience the "NO cartridge" error only happens when the printer's chip sensor doesn't have contact with a chip- for example, when no cart is installed, not installed all the way, or a cart is installed w/o a chip attached (which you NEVER want to do, because it can damage the sensor). Another reason the printer would give the "NO cartg" error would be if the sensor is damaged, but in this case, the error wouldn't go away until the sensor is replaced (no matter what cart or chip is installed), so I believe your sensor is fine since the error goes away after resetting the chip. If the printer's sensor has contact with the cartridge chip, but there's a problem with the chip, the printer would display an error like "Set ink cartg", or "Ink cartg error, replace cartg".
If the error goes away after removing the cart and resetting the chip (I assume you already tried removing + reinstalling, without resetting), but you have already replaced the chip, and have the same results with two chips, but all other positions are working well, and you have had good results with this cartridge for two years, I have to suspect something related to your printer, but an not certain what... You could certainly try a new cartridge, but I don't have confidence this will resolve your issue, because I don't think your current cartridge has a physical fit issue (or you would have had problems with it sooner, and I would think moving the cartridge would change the error), and you have already tried a new chip with the same results.
Sorry for not having a magic answer for your bizarre situation... please do keep me posted, as I'm very curious about this!