The simple rule for short run shut down in perfect competition is:

If P > AVC operate in the short run.: If price is above average variable cost for each unit produced and sold, the firm earns enough revenue to pay variable costs (since price is greater) and has added revenues to offset fixed costs as we showed graphically.
If P < AVC shut down in the short run.: If price is below average variable cost for each unit produced and sold, the firm earns less revenue than the added variable costs it incurs (remember it only incurs variable costs if it produces). Therefore, the added revenue is less than the added cost, so losses are greater than just fixed costs. Ahead we will show this graphically.