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.)

Similarly, if you're seeing a dialog regarding tags being added to or removed from items or items being added to or removed from collections on multiple computers, and the dialog is going off the screen, simply press Return to dismiss it. (This will be fixed in a future version.)

If you're correctly accepting changes and/or dismissing the tags/items message 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 fails due to an error, any selections you've made in the conflict resolution window won't be saved, and Zotero will display the same conflicts 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.