Hey there, Lindsey!
Welcome to the Apple Support Communities. From your post, I understand that the Lightning to 3.5 mm Headphone Jack adapter isn't functioning properly. Specifically, unless held in a particular way, the audio cuts out. I'm happy to help!
I see you've tested the adapter with two separate auxiliary cables and a pair of headphones, but the issue persists. Since those steps haven't solved the issue, I would recommend taking your iPhone and adapter into an Apple Store or Apple Authorized Service Provider to be inspected. A Genius or Apple-certified technician can determine what the issue is, and how to resolve it. Find locations, get contact information, and set reservations here:
Apple - Find Locations
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You can also reach out to Apple Support directly for more information and to review your options:
Contact Apple Support
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Cheers.