I have just installed a new extension for my Magento webshop. It's a count down function that shows when to order if the order is to be shipped the same day
When using the standard layout the extensions works: 
When I switch to my own layout rwd/default - the counter disappears:
I have installed other extensions and the all works perfectly with my layout. How do I fix this?
The best option is to contact the company that developed the extension and ask them for help.
Probably, what is happening is that this extension needs to insert layout files and they did in the default theme, but not in your custom theme.
If you installed this count down extension manually (not using Magento connect) you have the folders and files, so you could take a look and check if is something like that:
app/design/frontend/base/default/layout/your_extension.xml
If you find that, try to add this your_extension.xml file in:
app/design/frontend/[theme_company/[theme_name]/layout
Again, this is just an idea. Since I don't know which extension you are using, my first approach would be to contact the company that made it because the problem can be more complex than just add files. Good luck!
