The hand does persist
A successful save only changes whether/how the target is affected by the spell
The target must make a Strength save. On a failed save, the target takes 2d6 bludgeoning damage and is restrained for the spell's duration.
In fact, every spell persists for the duration even after a successful save unless there is specific mention of the spell ending.
A spell's duration is the length of time the spell persists... Some spells specify that their effects last until the spells are dispelled or destroyed.
[emphasis mine, note it only says some spells]
This is because the saving throws only allow targets to avoid effects of the spell rather than cancel the spell as a whole.
Many spells specify that a target can make a saving throw to avoid some or all of a spell's effects
How this works with other spells
For example, charm person will last the whole hour unless it is dispelled, even if the target succeeds on the save (although the spell then has no effect) since there is no mention of the spell ending otherwise.
You attempt to charm a humanoid you can see within range. It must make a Wisdom saving throw, and does so with advantage if you or your companions are fighting it. If it fails the saving throw, it is charmed by you until the spell ends or until you or your companions do anything harmful to it. The charmed creature regards you as a friendly acquaintance. When the spell ends, the creature knows it was charmed by you.
