Not sure if the problem still occurs, but we were facing the same issue and solved it for us. have a look at this solution: https://community.atlassian.com/t5/Answers-Developer-Questions/Issue-links-missing-from-REST-search-and-issue/qaq-p/530279
For others with the same problem: the problem depends on the visibility of the linked issues field in the field configuration of your project. It might be not visible!
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