I am also having problems with reminders not syncing between devices over iOS 7. However, both my iPhone 5 AND my iPad w/Retina have the problem. If I add to my iPad, it will show up in my iMac (running OS X 10.8.5) reminders but not on my iPhone. If I make a change on my iPhone, my iMac will sync but iPad will not.
As others have noted, if I make any kind of change to a reminder in whichever of the devices has not synced, it will force a sync at that time. But this is a "work around" rather than a "fix". I would greatly appreciate Apple fixing this issue in an update. I rely too heavily upon Reminders to have it be this buggy.
Also, none of the other proposed "fixes" in this thread have solved the problem for me.