Your assumption that things would improve was reasonable - these sorts of reactions generally do resolve after a time. At this point, though, the situation does warrant professional intervention, because it's progressed beyond the point of what might be regarded as 'normal' separation anxiety. Almost always in such situations there is nothing really problematic at school; rather, the distress involves the child's absence from the parent. Arrange an evaluation with a pediatric mental health professional who can evaluate your son and plan with you and your wife how to proceed.
Is he is second or third grade? Maybe something is stressing him out in school like more homework or assignments (third grad is pretty difficult and rewarding) MY son is 8/third grad and we have to do all of our homework together everynight (always been a ritual), if we miss a night he pouts, and pouts at school. He sometimes will get stressed out if an assignment isn't getting done on time and will cry because he wants to be so perfect in class.