I also have had problems with the maintenance plugins. What you can do instead (if you are familiar with HTML) is create a simple “Closed for Maintenance” page. Save the page as xindex.html. Upload the xindex.page to the same directory as your WordPress installation.
You WordPress installation comes with two files index.html and index.php. While you are working or doing maintenance to your site, first rename the existing index.html file as realindex.html then rename the xindex.html that you uploaded as index.html. This will replace the WordPress homepage with your maintenance page.
When you are finished working and are ready to display your site, reverse your steps. Rename the current index.html back to xindex.html and change realindex.html back to index.html. Sounds more complex than it is in practice, but it entirely avoids buggy plugins.
Here’s a link to my maintenance page. You can copy the source.
Closed for Maintenance