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Have you tried connecting your iPhone to iTunes and then rearranging your apps this way: navigate to 'Apps' category and double click on the screen from where you want to move any App and then drag it to the desired screen?
So, long press and hold the app icon to be rearranged and then drag it to the desired screen would be the standard approach. I'm not sure what you mean by "iTunes keeps dropping apps..."? cf. support.apple.com/en-us/HT200290