When a Classify Search Term Improvement adds a search term as a keyword, it uses phrase match by default. If the Google Ads campaign has Broad match keywords switched on, it only accepts broad match keywords, so the Improvement can't be pushed.
Check the setting
In Google Ads, open the campaign.
Click Settings.
Find Broad match keywords and check whether it's on.
Fix it
Either switch off Broad match keywords for that campaign in Google Ads, or change the keyword's match type to broad in the Improvement before you push it.