Look in your logs to see if piwik.js is being requested by those visitors. You want to rule out any bots or javscript-disabled users.
Then look for piwik.php requests from the tracker.
Look in your log_visits table.
And make sure you’re looking at the right day on your dashboard.
It’s amazing what walking away for a few hours can do. Turned out to be a firewall issue. Once I allowed port 80 through to the machine running Piwik, everything fell into place. Of course, all my machines have full access to machines on my network, which is why it worked for me (and only me).