The credit for this article goes to @xrobx99. I wanted to blog about his discovery so that others might find the solution quicker.
We have an Cisco ASA that we had to reboot every month because the memory would keep growing. We thought it was a memory leak (and it may have been in previous revisions), so we just lived with the fact that we had to keep rebooting the ASA to clean up the leak. @xrobx99 found that by default the ASA caches html when using webvpn. Well that explains that! A growing cache could easily be misinterpreted as a memory leak (see CSCtb68311)!
webvpn cache disable
Our memory use has not grown since making the change!