Hi NickNick56,
Welcome to Apple Support Communities. We'd recommend starting with the general guidance in Connect external storage devices to iPhone to make sure that everything is set up properly. Then, isolate as much as possible by testing multiple cables if available. If possible, testing your card reader with another device or another card reader with this iPhone would help narrow things down as well.
If you have an accompanying app installed on your iPhone, take the steps in If an app on your iPhone or iPad stops responding, closes unexpectedly, or won’t open for that app. There may be an update for the app to accompany the latest iOS version. Guidance below is from that same article.
1 Close and reopen the app
Force the app to close. Then open the app to see if it works as expected.
2 Restart your device
Restart your iPhone or restart your iPad. Then open the app to see if it works as expected.
3 Check for updates
To see if updates are available for the app, open the App Store, tap your profile icon, then scroll down to see if updates are available. If updates aren't available for the app, update the software on your iPhone or iPad.
4 Delete the app, then redownload it
Delete the app. When you do this, you might lose data that was stored in the app. Then redownload the app. Then check to see if the problem with the app is fixed.
You may also need to check with the manufacturer to see if there is a firmware update and further troubleshooting. If you have the paperwork that came with your device, contact information should be included. We did a search and found the following page that might also help - Contact Us - Vivitar.
Cheers!