Open the settings app and navigate to the General > Storage option.

Here check if you have a good amount of available storage left.

If the storage left is below 5 GB, you must delete some photos, videos, multimedia, or apps to make space.
Method 4: Change the audio quality
Audio quality plays an important role when you are recording through the Voice Memos app. By default, the Voice recording settings quality is set to compress which is causing most of the issues.
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Open the settings app and navigate to Voice Memos settings.

Here go to quality settings and make sure to choose the “Lossless” option.

Once it is done, restart your device and see if it helps to fix the issue.
Method 5: Disable low-power mode
iPhone comes with a low power mode, so you can save up some battery while the battery is low. This is a great feature, but simultaneously, it limits your iPhone’s functionality. For example, it will stop any background recording task to save battery. This is exactly why you’re facing the issue of Voice Memos Not Recording Audio on iPhone 14, 14 Plus, and 14 Pro Max.
To fix this, make sure you disable the battery-saver mode. You can do this by going to Settings > Battery and disabling the “Low power mode” option.
Method 6: Turn off the sound recognition feature
iPhone also has a special sound recognition feature that helps detect sounds and perform actions on them. But this feature is quite buggy and is also causing the Voice memos sound recording issue.
To disable this, open the settings app and navigate to the accessibility option.

Here go to the sound recognition feature and disable it.

Once done, please restart your iPhone and see if it helps.
Method 7: Use third-party voice recording apps
If none of the above methods help you much, then you might have to use other third-party apps until Apple releases an update for the app. This can be frustrating but holds good as a temporary solution to the problem. There are multiple free to use voice recorder apps that are available in the App Store.
Method 8: Check for hardware damage
If none of the above methods help you, then most probably your device is facing a hardware issue related to the microphone or the Audio IC chip. When this hardware issue happens, you will not be able to record anything, calls will not work, camera video recording will not work, or the voice memo app will not work. So make sure you set up an appointment with the nearest Apple care center and get your iPhone checked for hardware issues.
Conclusion
This brings us to the end of this guide for fixing Voice Memos Not Recording Audio on iPhone 14, 14 Plus, 14 Pro Max. Please note that the app itself may not have any issues, and you can fix any temporary technical glitches by simply restarting your iPhone. But you might have to schedule a repair appointment with your nearest Apple care center for hardware issues where the microphone is damaged, or the Audio IC chip is damaged.