Unless they are misused, spring joint calipers require little in the way of maintenance.

You should occasionally oil the moving parts of your caliper (the adjustment nut, threaded rod and the spring).

Be careful not to oil your caliper too much, as this can cause the moving parts to become too loose. You should be able to adjust the width of the legs of your caliper easily, but you should also be able to feel friction between the parts.

Avoid using your caliper to measure moving parts of machinery, as this can affect the shape of its measuring faces, and therefore the accuracy of your measurements.