Hey Dan.
This guy is busting his butt trying to figure this out. His reply in regards to your suggestion was:
There are so many javascript files in their Gantry theme and I can not look at it one by one. Adding some custom css rules specifically for the theme seems to have fixed the issue.
Unfortunately after some testing we determined the CSS 'hacks' did not resolve the issues. Instead it created more issues.
Can you look at the link I sent and at least suggest a Gantry javascript file that may be causing the conflict? This would expedite things getting resolved correctly instead of hacking unrelated files all over the place.
You guys have access to all the resources and I'm stuck in the middle trying to deliver a working Website.
EDIT
When you visit the page I linked to, be aware the dev has updated his files and this has modified the layout - as I mentioned he was forced to hack CSS to fix the disappearing buttons.
With the new update there is now a gear icon within the "Enter a Location" field. Clicking on this icon demonstrates the issues we are having - clicking anywhere else and the gear icon disappears.
Here is the devs response:
The gear icon in the location field disappears only with the Gantry theme and we're really having a hard time why this happens. It may be better if you ask the developers why they have added this effect to dropdown buttons.
As I mentioned, this guy is going out of his way to hack/mod his plugin to work around Gantry. In my opinion this should not be necessary. I did a vanilla WP install and this guys plugin worked flawlessly. I then installed Gantry with no additional plugins and issues appeared immediately.
If you guys need some money, I'll gladly kick out a reasonable amount to get this resovled. That is how desperate I'm getting to deliver this client Website.