I too have had this problem.
WIndow 7 64, all patched up.
I usually use Firefox, and it would crash a lot when I was at iCloud.com. The error happens mostly when I change to the Address Book or Calendar. I got a javascript error that would ask me if I wanted to stop running the script. I have seen this error in other threads, and not seen an answer...other than install Safari.
Which I did, and now get bascially the same kinda crash, but it is with the Web2Kit. Safari will restart, and it has happened mostly when I am writing a new email. Thankfully I can find most of the email in the Draft box.
It just makes me wonder if the two crashes are related.
Both crashes in each browser will stop the browser from getting Push notifications about new email messages and I have to manually refresh the browser to get newest emails until I either kill all browser proceses or restart the computer.
To be honest, as much as I keep iCloud open via a browser, I wouldn't mind a self-contained full-blown iCloud application like say Outlook. (Yes I know I could run and sync Outlook, but gave up on those two playing nicely together as well). Accessing iCloud via a browser on WinOs seems very buggy.
A self-contained App would be nice so all the plugins and other script tools wouldn't crash it, and we could use the web browser access in a pinch if we wanted to access from another computer.
I have tried disabling the RSS feeds as well as the Java to see if the Web2Kit will stop crashing randomly though.