In the short run, a perfectly competitive firm will continue to produce even though it might experience an economic loss if

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In the short run, a perfectly competitive firm will continue to operate as long as it can cover its average variable costs, even if it's not covering its total costs (including fixed costs). This is because, in the short run, fixed costs are sunk costs and the firm would rather cover some of its costs than none at all. If the market price exceeds the average variable cost, the firm can cover all of its variable costs and contribute something towards its fixed costs, even if it's not making an economic profit.

In the Short Run, a Perfectly Competitive Firm Will Continue