Do you have FTP or can you get into your site in cPanel? Try this.
Do the update. DO NOT leave the page.
Go into your site and download a copy of the Alidropship plug-in that you just loaded.
http://yourwebsite.com/wp-content/plugins (download "alids" folder.)
Now leave the page and CLEAR YOUR CONNECTION. Make sure that you are NOT connected with the "do it again" problem. Logout and log back in to make sure you are not receiving the do it again message. When you know you're good then log out again before proceeding.
Go back to your FTP or cPanel and DELETE the alids folder.
Login to your website to see that the Alidropshop plug-in is not listed and, then log out again.
Go back to your FTP or cPanel and upload the alids folder that you downloaded to replace it.
Do NOT be logged in to your website when you are doing this.
When you have uploaded the plug-in folder log back in to your website.
Check the version number for Alidropship to make sure it's v0.9.20.1
Hopefully this will work for you. Good luck with it.
Incidentally, just to cover my own behind you acknowledge that you are doing this
at your own risk.
Even with this simple operation I urge you to make a BACKUP before doing anything. Things can go wrong, we all make mistakes.
If you're not experienced with FTP or changing something in your website through direct access then DO NOT DO IT!
I am NOT a support person here I'm just another Alidropship user trying to give you a hand.
I assume no responsibility for anything that may happen if you decide to follow this suggestion.