The best summary of the issue is at the Delight blog (the people who do the great firmwares):
You may have noticed that some Symbian apps like cuteBox, Dropian or FilesPlus can't login into Dropbox anymore.
I recently read multiple reports about this on Delight Blog, Symbian Forums or via Email. Most of them claimed a bug on Delight side, but that's not true:
Some users tested it on original firmware(s) or other custom firmwares like The One by Daniel or Mohican by Xeon, all have the same issues, the problem can be a:
a) reboot directly without of a usual shutdown (like a system application crash or stack overflow)
b) like a) but with a reboot loop
c) simple app crash
d) full freeze of the phone
If you try to login with your Dropbox account inside of the apps. Thanks to the testers (like Allstar Software, Ade and Adan from Symbian FTW and Matthew from the comments below) for these informations! The mentioned applications are QtQuick based GUI apps which use QtWebKit to show the login page, so the issue must be there.
My guess about this: It seems like it's a QtWebKit bug which was unknown before and recent updates on Dropbox's login page uncoverd it. It affects Symbian Belle Refresh and FP2 and Anna.
All of which is a major shame, though perhaps such showstoppers were inevitable, given how complex smartphone operating systems are - and with no one left to patch/support the guts of Symbian/Qt, we're rather.... err.... screwed.
Note that you can still log into Dropbox using Web or Opera Mobile (etc) - just as long as Qt isn't involved. So you can still grab that file in an emergency. But you can rule out all Dropbox clients for logging in.
As some people have pointed out, if you'd previously logged in with a client then you may have an authentication token which will work for a while. But not forever.
I'm mulling over a few editorials - watch this space.