Your Shopify store theme/apps will dictate when the 'sold out' label appears. If you've got positive inventory for the products your trying to show, I think it might be something less obvious. I found this Shopify thread, it mentions that some themes will list products as sold out even if they have just one variant with 0 inventory.
The threads mainly about specific apps causing this behaviour with their settings, have you installed a new app recently? that might be causing this?
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