imessages on my mac stop syncing with my iphone

Messages > Settings > iMessage on the Mac, there's a Sync Now button, hit that. Check the same screen shows your phone number ticked, not just the email. If it keeps falling behind, the Mac is probably asleep with the lid closed and only catches up when it wakes, plugging it in and leaving Messages open helps. Signing out of iMessage only (that screen, not the Apple ID) and back in rebuilds the sync, and that tends to stick longer than a full sign out.