Work down this list. One of these is nearly always the answer.
An invisible space
Copying a key out of an email very often drags a space along with it, at the start or the end. You cannot see it, but the check fails.
Paste your key into a plain text editor first. Remove anything before or after it. Then copy it again and paste it into the plugin.
This is the most common cause by a wide margin.
You have used all your activations
Each plan covers a set number of websites: one for Single Site, three for Business, twenty-five for Agency.
Open the License tab. It tells you how many activations you have left.
If it says none, you have two options. Go to a website you no longer use and click Deactivate license there, which frees the slot. Or move up a plan.
Staging and development copies count too, which catches people out. If you have activated your key on a staging site and then again on the live site, that is two activations.
Your host is blocking the connection
The plugin has to reach our server to check your key. Some hosts block outgoing connections by default.
If you suspect this, ask your host whether outgoing HTTPS requests are allowed from your site.
Your license has expired
Open the License tab and look at the expiry date.
If it has passed, your plugin keeps working. Payments carry on, your customers are not affected, and your data is safe. But after a grace period the settings pages lock, and you stop receiving updates.
Renew, then click Re-check status on the License tab.
Nothing works
Message us. We can see your license from our side, and we will sort it out. This is not something you should spend an afternoon on.