NO!!!!
The CF is still installed (in Flash), it's not "gone" – the CF is giving you the "install WebIF" web page (no CF, no web page). If the CF had re-installed from your UPD (if you accidentally had the .hdf file on it), you would see a screen (TV) telling you the firmware install had completed and requiring you to restart. Then it would find the WebIF still there (which is on the HDD, not in Flash). When the unit reboots, you'll see the CF version displayed on the VFD – that's more evidence the CF is still there.
You need to recognise the difference between the Custom Firmware (which is a modified version of the Humax firmware, installed in Flash memory using the firmware update process), and the packages (software) which (mostly) exist in the file system on HDD. The CF
enables the packages to be invoked, and it is the packages which provide the bulk of the functionality. WebIF is just a package (and in theory you could write your own alternative WebIF).
This is just a coincidence. The UPD is not responsible for CF not finding WebIF. If CF can't find WebIF it assumes the CF has only just been installed ("Custom Firmware Successfully Installed") and you need to proceed to the next stage (ie downloading the WebIF and its dependencies).
The real question here is what has happened that WebIF has gone missing, and the fact is your report indicates a problem with the HDD. It might be cured by a
fixdisk, but my hunch is something more serious.
You've been around long enough, did neither of these occur to you?:
Steps for Resolving HDR-FOX Crash/Reboot Issues (click)
Quick Guide to Disk Recovery (click)