No, it's quite possible. I've just never used it as a desktop reminding tool - If I have a reminder set on my palm, my palm can tell me, I don't need the desktop tool blathering on about it at all. Think I turned alarm notifications off entirely on the desktop, now I think of it. ;)
Maybe it's Agendus. I could try removing that temprarily - but I think it's always done that... Even before I used Agendus.
It's more than likely a setting or corruption that I've carried from PC to PC, ever since my first Palm III. :-)