My APP check update by comparing local version and remote version returned by iTunes lookup API. But the API still return old version after new version has released.
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I was also facing same issue but in my case I was using http (e.g. http://itunes.apple.com/lookup?bundleId=com.xxx.xxxx) so not getting latest app version. Then I replaced http to https (https://itunes.apple.com/lookup?bundleId=com.xxx.xxxx) after that its working for me.
Update - Our team sent mail to apple developers and ask why https is working and http is not working and got reply from apple team. He told "In general, there is a 24 hours delay for updated app information to go from App Store Connect to the public."
For more information see their email reply-