This goes for those colored German dice you can order online, or BoardGamesMaker dice (they paint/print the design right on the die). APPLY A CLEAR COAT OF VARNISH TO THE DESIGNS. Perhaps an acrylic satin varnish as sold in popular hobby stores.
Do this as soon as possible, as over time the oil from your hands (or simple storage in a clear plastic container) can cause the paint to get "gummy" and even pick up lint or rub off. Cleaning it too aggressively with liquid soap can also cause the image to rub off. This process can take about a year but will happen if you don't apply some protection to it.
Glossy finish plastic dice seem to have this problem worse than the "matte" finish dice but it is still a concern.
We all recall the classic wooden dice yellowing with age and the black paint rubbing off through use by sweaty hands, so wooden dice aren't immune either.
This is one strength of inscribed plastic dice, even if I have some issues with the Mythic tier (remake) quality control... (the inscribing process was a little inconsistent especially for the lion shields).