Same here. This worked for me, hopefully for you too!
Follow the instructions provided by this link tom Shopify support on the issue:
http://support.modalyst.co/en/articles/3351232-how-to-fix-sold-out-issue-on-shopify
Note: ONCE YOU CHECK THE BOX for Shipping YOU MUST SAVE BEFORE Clicking ‘View Inventory’.
THEN:
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Pay attention to whether ANY VARIANT OF ANY ITEM HAS ZERO (0) INVENTORY. Apparently if ANY VARIANT HAS ZERO, ALL SHOW AS SOLD OUT.
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Change the Available Quantity from ZERO to ONE in any item/variant with a zero. NOTE: Make sure you have inventory for some variant of the product or you’ll have some upset customers.
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Check your website to see if it worked! Hopefully So!
Ick