Hello missyi501,
Let's use the steps below to restart your iPhone:
1. Press and hold either volume button and the side button until the power-off slider appears.

2. Drag the slider, then wait 30 seconds for your device to turn off. If your device is frozen or unresponsive, force restart your device.
3. To turn your device back on, press and hold the side button (on the right side of your iPhone) until you see the Apple logo.
You can find those steps in this resource: Restart your iPhone - Apple Support Your contact can also use the steps from that resource to restart their iPhone as well. A restart can sometimes help address odd behaviors.
Should that persist, do messages you receive from that contact also get delivered as SMS instead of iMessage?
Is the email and phone number details correct in the Contacts app?
Let us know, and we'll keep moving forward based on those details.