My husband and I filed for divorce, but about halfway through the process we had sex together. Does that mean we have to start over again?

No, you don't have to start all over again, unless you remarried.

A reconciliation should immediately stop a divorce which is in  process (that is because your Petition asking for the divorce has stated that the marriage is insupportable - can not survive - and your behavior regarding reconciliation states otherwise). However, having sex does not mean there has been a reconciliation.

A reconciliation means the parties have begun living together and, therefore, they no longer have irreconcilable differences or find the problems of the marriage insurmountable. By reconciling, they have disproved the basis of the divorce petition, so a divorce should not be granted.

 If a divorce was already granted, the parties are not automatically 'remarried' unless they, again, fulfill the common law definition of marriage, or commit to a marriage ceremony.

Living together, however, should impact on the alimony and child support payments (if s/he is providing for mortgage, rent, food, etc., why should that person also pay for 'support' ?   That is an argument the one paying support can make to the court in order to have support stopped or to get a credit for the months the parties cohabited. However, the divorce was finalized and does not have to be 'redone').

In contrast, having sex does not mean that the reason for filing for a  divorce no longer exists. Whether during the process of divorcing or after a divorce, having sex should not impact any orders or request for court orders.