Sounds like a couple of problems or combination there of.
A. One coat of paint is not completly dry (cured) when next coat is applied.
B. Putty is applied too thickly or is not completly dry when painted.
Although paint is dry to the touch within a few minutes, it can take up to 48 hrs to completly dry. Basic test is to smell the paint - if you still smell paint fumes, it hasn't cured yet.
Putty will shrink while drying and like paint takes some time to cure. If you sand it before it's cured, it will continue to shrink, causing sinkage and cracking. If you apply several thin coats, they will cure faster with far less shrinkage/cracking than one thick coat of putty. Just take your time and don't get into a hurry.