iCloud on the web is missing events on iCal, iPhone and iPad

I am using iCloud to sync 3 calendars between my Mac, iPhone and iPad. Bizarrely, all of the events are perfect in iCal on my Mac as well as on the iPad and iPhone. However, when using iCloud's Calendar app on the web it is a patchwork of random events missing. There seems to be no rhyme or reason to it.

Also, with iCal running on the Mac, my Calendar app of choice, Fantastical, displays all of the events perfectly. Once I quit iCal, I get the same random missing events as the web app. Yet, Calendar, Fantastical and any other calendar apps on both my iPhone and iPad always display all the events properly.

This has been driving me crazy. I tried exporting all of my calendars locally, deleting everything on iCloud, creating new calendars and merging in the old data. I got the same end result. I also tried importing the old calendars as completely new ones (not merged) and got the same missing events.

If anyone has any suggestions of something I may have missed, I would be eternally grateful. I can't afford to lose any of my calendar data.