Evaporated Milk Has a Long Shelf Life.
Cans of unopened evaporated milk, which has about half of the water found in regular milk, have a much longer shelf life than their water-containing counterparts. Because of this, you might assume that this extra long shelf life applies even after the can has been opened.
An Open Container Makes It More Perishable.
When the container is opened, the seal is broken, and air reaches the product rendering the long shelf life useless. Now, exposed to the air, the evaporated milk will act more like regular milk and, in fact, the former will actually spoil faster.
Bottom Line
The leftover milk should be stored in the refrigerator in an opaque covered container. It should not be left in the original can or stored in a clear plastic container. If you store it properly, you can use the remaining evaporated milk for up to 3 days, but always discard the leftovers after this point.
References
Shelf Life Advice: How Long Can I Keep Evaporated Milk, Sweetened Condensed Milk, and Powdered Milk?