First, be sure you're not cancelling the conflict resolution process: you need to click Next/Finish in the bottom-right corner of the conflict resolution window after making each change. If you don't see a Next/Finish button, you may need to enlarge the window. (This should only be an issue on computers with low-resolution screens.)
If you're correctly accepting changes but are still seeing the same conflicts over and over, you're likely receiving a sync error, which should be indicated by an error icon to the left of the sync icon in the Zotero toolbar. If a sync of an item fails due to an error, any selections you've made in its conflict resolution window won't be saved, and Zotero will display the same conflict again the next time you sync. To address the root problem, you'll need to examine the error message and, if necessary, post a Report ID to the Zotero forums. While troubleshooting the problem, it may help to temporarily disable auto-sync in the Sync pane of the Zotero preferences.