I never remove it either. When it starts drying out, then I apply, on top of the original grease, one drop per link of Boeshield T-9. I've never had any reason to change this practice. My chains all work superbly (I use SRAM on all my bicycles), and they last a good, long time.
In fact, I just purchased a SRAM/Sachs/Sedis PC-7X on my 3-spd PUCH. Smooth as anything I've had. I wonder how long this one will last...