I guess you meant to say "each time the form is opened"?

you want to track a form, you will have to set up a database to hold the
data. Since working with infopath and databases is relatibly easy it
should'nt be a problem - just create a database (or a sharepoint list, or an
xml document) and a stored procedure that adds 1 to a value (or .net code
etc) and call that procedure when the form opens.