If a spell requires concentration and allows repeated saves (e.g. hold person) each round, choose one or the other:
1. You choose concentration. Saves are not repeated (or auto failed).
2. You choose NOT to concentrate or lose concentration. Saves now repeat.
So, with hold person, the cleric could cast it and choose NOT to concentrate, but then the target gets to save each round to shrug off the effect. If the cleric chooses to concentrate, then the target (after failing the initial save, which is always allowed!) would NOT get to make saves unless the cleric drops concentration.
For something like flesh to stone, if you concentrate, the target WILL become stone after three rounds. However, if you lose concentration, the target begins making saves normally, but with each concentrated round being an auto failure...