Verify you’ve followed the steps to accept the invite:
Accept an invitation to control a home
When someone invites you to control their home, you get a notification in the Home app on your iOS device or Mac. Follow the steps below to accept the invitation.

On your iPhone, iPad, or iPod touch
- Open the Home app and tap
. - Tap Home Settings.
- Tap Accept, then tap Done.
After you accept the invite, tap
, then tap the name of the Home to control it.
On your Mac
- Open the Home app and click
in the toolbar. - Click 1 Invitation.
- Click Accept, then click Done.
After you accept the invite, click
in the toolbar, then click the name of the home to control it.
Share control of your home
https://support.apple.com/en-ca/HT208709
Aside from that you could try restarting the device you’re trying to accept from and reset network settings to eliminate any internet issues going on.
And ...see if there are interruptions in service in your country or region on the the Apple System Status page