Hello @Lyndsaytyler
Thank you for posting about this. Yes you should be able to access downloaded routes offline. I'd like you to try an uninstall / reinstall of the Strava application, as this usually resolves this issue.
Please go ahead and delete the Strava application from your phone. Power your device off for 10 seconds, turn your phone back on and reinstall the Strava application. You will not lose any data if you do this since all data is stored on the Strava servers.
Google Play Store:
Strava: Track Running, Cycling & Swimming
How to update your apps on Android: Support - Google
Apple App Store:
Strava: Run, Ride, Swim
How to update your apps on Apple: Support - Apple
Please let me know if this doesn't solve the issue and sincere apologies for the inconvenience.