Hmmm… When there are no usage stats log files, it seems to be a problem with logging the usage events…
Are both your plugins, Usage Event as well as Usage Statistics, still enabled?
Also, please double check your usage stats folder permissions, so that web user can create, move, write (new) files there.
In what logs did you see the 404 error?
Did you maybe change anything on May 19th or 20th?
What do those schedule task logs (after May 20th) contain, how do they look like?
Do you have those log files after May 20th in your folder usageStats/usageEventLogs/ ?
Do you have a log file with the current day (today) there? I.e. is the usage still correctly logged?
Do you use Acron Plugin or have you set up a cron job (for those scheduled tasks)?
I use acron. Also, there are no files in usageeventslogs folder.
Also 20th was the last day when the file was made and stored in archive. The next file (21st) created problem and was not in archive folder. I think it was in some other folder. I opened the file and deleted everything in it (a week later) and the file was then passed to the archives. But no new file was made even thereafter.