I think what you are looking is what is often called "change data capture". There are products to do this, but I hope you (or your client) has plenty of money to spend, because it won't be cheap - at least a few hundred thousand dollars.
Products you can look at:
* IBM Infosphere CDC
* Oracle GoldenGate (or maybe XStreams)
* SQL Server - has some built-in but you'll need to roll up your sleeves. 3rd-party products may be warranted.
There are a number of 3rd party products, google CDC or "change data capture".
I participated in a project for implementation of the IBM product. It did work, but was problematic to resync if a database went down. At least, that is what the DBA told me. Otherwise, no real problems. What you do with the changes you get will be up to you. So for example, if you have currently have transformations in your ETL stream, you may need to re-architect or refactor components so they can be called upon to do incremental updates. This can be very minor or a project itself, depending on your warehouse and ETL. If you lack experienced ETL staff, you may want to bring in some consultants to help.