I added Minimum Price but repricing goes below it

Adding a Minimum Price to an item in the inventory database does not automatically prevent the repricer from going below it. You must also set up a lower limit based on the minimum price in the reprice schema you are using on that item.

In Step 3 of the Reprice Rules Wizard choose to add a new lower limit and set it to be equal to (or higher/lower than) the Minimum Price. Finish editing the schema and reprice the item once again to see the results in the inventory grid and Reprice Log.