Typically this occurs when Word is using an Access or Excel data source with
a DDE connection - in that case it has to start the Access or Excel program.
Several things can go wrong, e.g.
a. Excel or Access may be set up so that they do not accept DDE connections
(have a look at the Tools|Options for each program
b. Excel or Access may run a macro that prevents the connection from
completing, or display a dialog box which the user needs to respond to.
Sometimes these dialog boxes are not visible unless the user ctrl-tabs
through the available Windows. In particular, this would happen if the merge
data source is an Access parameter query.

There are other possible problems (e.g. DDE seems to be particularly
unreliable on some systems) but those are the ones I would look for first -
which version of Word are you using and what is the data source?