In an unanimous ruling on December 8, the justices said that although the laws of New Hampshire grants the state the power to grant divorces- it lacks the authority to undo a divorce once it is final.
Although a few states allow divorces to be vacated under some specific circumstances, most states, have no statutory authority to "undo" a divorce.
Although it is nice to see a couple patch things up, divorces are considered a one way street. The finality of a divorce is generally good for the parties and sound policy for the public. We want people and the rest of society to know that the divorce is final and irreversible. We don't want to be creating a mess with inheritances, new marriages, child support and all the other issues that depend on the marriage status being very clear. This policy may not be romantic, but it is highly practical.
In Texas, there is no going back after a certain point. If thirty days has expired since entry of the final decree, then you are out of luck. After that, the court generally loses any power over your divorce case (if you have children- that is a different case and they keep power over your kids), But if you are within the thirty day period, you could file a Joint Motion for New Trial. If that is granted then you both can dismiss the divorce case. Aside from that, if you want to be husband and wife, you will have to remarry.