Mike,
I'm a bit confused with the different pages and redirections you're mentioning
Generally, there are "User Profiles" and "Facebook Pages":
* User Profiles are meant to be 'individual' pages and not meant for really promoting a product, business or other item. A User Profile is meant for making 2-way connections with other users (friendships).
* Facebook Pages are one-way communication channels where anyone can "Like" the page. Then, the Facebook Page can push information out to their wall and the user's that Like it. Pages are meant for businesses and products.
The Subscribe button (which coincidentally is being changed by Facebook to be a "Follow" button due to common confusion of it's purpose) is meant for "User Profiles".
The JFBCLike or JFBCFan module can be used for Facebook Pages.
So, hope that explains a bit more about the different types of pages available from Facebook.
Beyond that, for the Like button going from 0->1->0 quickly, what URL is the Like button pointing to? Can you post the URL the Like button is on or the URL you've set in the Like button parameters that is to be Like'd? That problem is usually easy to fix by running either page though Facebook's URL Debug tool and looking for issues:
developers.facebook.com/tools/debug
Hope that helps,
Alex