The first zero is getting dropped because it isn't really there - your cell
has just been formatted to show one. To format your merge field so it will
do the same thing - open your mail merge document, press Alt+F9 to show field
codes, for your zip code field, add the following switch after the field name
and before the bracket:
\# 00000
if your zip code field name is zip - it would look like this:
{ MERGEFIELD zip \# 00000}
Alt+F9 again to hide the field codes - when merge data is displayed, you
should have your leading zero's back.