Store your seal ink in a non-porous container. In Chinese these are called yinnihe 印泥盒. Porcelain is most commonly used in China though any glazed ceramic, glass, lacquer, or metal container can be used—anything that doesn’t absorb the oil from the ink and dry it out. The container’s lid doesn’t need to be airtight, but do keep the lid on when not in use so the ink won’t dry out.
Since good quality ink in a lidded container can last for many years, find a functional container you can enjoy.