Use a smaller font.

That will happen if the row height is set to Exactly and isn't tall enough
for the font you are using. To see this in action, select the text in the
row that's being cut off, then press Ctrl+[ to decrease the font size one
point at a time. At some point, the descenders will be visible. If you press
Ctrl+] to increase the font size, at some point, the descenders will begin
to be cut off, and eventually, the upper parts of letters will be cut off.
The bottom line is that if you use a fixed row height, then the maximum size
of the font you can use is limited.

If this wasn't happening in Word 2003, then I suspect that you were using
different settings in Word 2003. It certainly happens in Word 2003 here.