Mentor Graphics' policy is to support the current release and two releases back. This is independent of the tools you are using.
In your specific case it means that DC2007.3 is not within the range of the supported releases. The last release that is supported would be DC2007.8 (or DC2007.7 if you would consider EE7.9.1 as a minor update).
Design Capture is not EOL.
However, we see a lot of customers migrating from DC to DxDesigner, specifically because they want to take advantage of the tight integration, schematic and constraint management concurrency, scripting and automation, non-Windows platform support and a number of other enhancements over the DC flow.
Thanks for your answer Joe. For me it's a bit confusing becasue when you look into the mentor main product page you won't find DesignCapture at all. It looks like for new customers who are interested in Expedition Flow Mentor is offering DxDesigner as a front end tool and is the only choice they have.
DxDesigner is not the only choice. But its the preferred choice, due to all the differentiated capabilities listed above.
Pretty much all new customers of Mentor Graphics are choosing Expedition Enterprise with DxDesigner as the design creation environment.