As I recall, I have had issues copying and pasting sheets (or cells?) in Excel that had cells with more than 255 characters, and I would get an error in Excel indicating as such. I don't know if this was fixed in Office 07 or 10, but the issue you are experiencing may be an Excel limitation.
We use Excel 97-2003 and Excel 2007 formats (.xls and .xlsx). In Excel 97-2003 the cell size limit is 32,000 characters, but only 1024 will be displayed. In Excel 2007 the cell size is also 32,000 characters, which can all be displayed.
So Excel can handle it but for some reason JMP assumes we're back in the stone age :).