If the dowry is deferred at the time of marriage, and the time given expires before it is paid, does the marriage become invalid? Also if the dowry is not paid, is the woman allowed to withhold relations pending the payment of the dowry?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Delaying the Mahar (bridal money) wholly or in part is permissible. In case of delay it is considered as a debt and the husband has to settle it later. If he does not pay it at the fixed time, it does not nullify the marriage contract.
Therefore, the wife should maintain conjugal life with her husband, while demanding her right (Mahar). There is no contradiction between being with him and demanding her legal right.
As long as she has approved her husband's request to delay the Mahar and to enjoy her at the time of marriage contract, she should continue that agreement.
On the other hand, the husband must pay the Mahar to his wife. Allah Says (interpretation of meaning): {O you who believe! Fulfill (your) obligations. …[5:1] Allah also Says (interpretation of meaning): {And fulfill the Covenant when you have covenanted, …}[16:91].
Allah knows best.