It's waiting for a response to an Ajax request to fetch some data from the Humax.
This can be delayed because access to the database requires getting an exclusive lock, since SQLite doesn't have sophisticated locking built in. The two tables of the TV Diary page share this lock with the background tvdiary_status which monitors what videos are being recorded or played.
In normal use they should all play nicely together. There's a 15 second timeout waiting for the lock, after which the request should fail, and you should get an error instead of Processing request...
Fetching the table data can take longer straight after installation because it builds a cache of details of the videos you have saved. On first installation it'll be getting the title and synopsis on all of the videos, but thereafter it'll only access newly added videos, and so be pretty fast.
Do you have a large number of saved videos? Or have an unusual file system, linking to videos on other devices?
If not, I would expect the processing request to change within a minute.
If the Humax crashes or the network goes down it may take until the browser times out the request.
It could be worth checking the tvdiary.log under Diag too, to see if it's getting locking errors.
Ah. I just saw your thread on 4TB disk.
I tested by filling my entire 1TB disk with videos to check the performance, and checked that USB & network drives don't appear under "/media/My Videos". But if external disks get involved it's just not going to work reliably.
I'll add an issue to the list, to allow the inventory to be disabled if desired.