Hi there,
Generally there shouldn’t be any difference in the tracking depending on the time of day. There is often a delay for when the tracking data shows up in your dashboard (generally it’s recommended to wait 24 hours).
Have you tested by visiting your site from an incognito browser window where you aren’t logged in, after midnight. If you wait for 24 hours does that tracking show up in Google Analytics?
Besides that you might want to confirm that you don’t have any custom filters setup on your Google Analytics account which could prevent some data from showing up.
Or I would suggest to use the Tag Assistant in Chrome to see if you can find any warnings or errors which might show up.