Word – Text in a table disappears before wrapping

Windows Vista Home Premium with Microsoft Office 2010.

I have a table in Microsoft Word where the row size is not specified, but the columns are fixed. When I type text that should wrap, it instead continues, invisibly, beyond the end of the row and then wraps 4 or 5 characters later. So the table looks like this:

|this is text in the 1st cell|This is the 2nd cell which |But this cell doesn't |
|                            |has wrapped appropriately, |where it should.      |

The word "wrap" is missing after the word "doesn't" in the 3rd column. If I insert spaces at the beginning of the cell, I can watch the word "wrap" appear on the next line, while "doesn't" begins to disappear. It's like the table thinks the column is a few characters longer than it is so it wraps too late, but can't show those characters that are beyond the end of the column.