So I have a specific database that won't release and shrink its log files. The DB backups are happening successfully, but I still have 4GB of logfiles (and no, this DB does not generate 4GB of log ...

Keep the backups! Then in the SQL Management Studio shrink the log file sizes. They won't shrink by themselves. From then on, run regular SQL backups and the logs won't get big.

Overgrown transactional log files can turn into real problems if they are not handled properly. Today SQL Server consultant Tim Chapman discusses the perils of not handling SQL Server log growth ...

You can use the following steps to shrink the transaction log file to a reasonable size (then be sure to implement the steps in my previous blog post to prevent this from happening again).