After updating to iOS 11, many people noticed that Voicemail Transcripts were missing.
For some reason, the issue is linked to Siri.
To fix missing Voicemail Transcipts,
Go to Settings > Siri & Search > and turn on 'Press Home for Siri'.
Restart your iPhone by holding the home button and sleep/wake button (upper right side) for 10 seconds.
Check your Voicemail Transcripts. They should be restored.