iCloud Calendar events disappear and reappear on my PC

I am a virtual EA in charge of calendar management for my clients. Yesterday I booked an appointment for a client, at the time that I booked the appointment there were NO appointments/events on my screen. This afternoon, I was told that I had overbooked an appointment for him. I am extremely careful about ensuring complete availability on his calendar.

I'm not sure why, but it appears that Calendar events are disappearing and reappearing on my PC (he uses mac/iphone/ipad). When I logged back into his iCloud today, not only was his event for today showing, but an event I scheduled yesterday was no longer there. I logged out and back in and the event I booked was back again.

Help me out with figuring out why this is occurring. Are there settings I should be changing to prevent this from happening? I schedule him in month view, so being in week/day view is not a problem.