I left it on Charlie last year but he got really scabby (with puss - it was gross) around the lines of it, that's why I was thinking it may be better off.
Also under the saddle area is where they sweat the most so not really sure what the advantages of keeping it on are, please enlighten me!
I take it off - Dyl has sheepskin numnahs, plus someone told me that it's a hangover from the days when horses didn't wear numnahs, and what's the point of leaving it on as that's where they'll sweat most?
But, in truth, it was just so I didn't have to fiddle about with any more lines than I absolutely have to.
I leave it on, not a full saddle shape, just a 'lozenge' on the top. I think it offers a bit more protection especially at the end of the winter when their coat goes a bit brittle. I know several horses who get little scuff marks from the back of the saddle there (saddler confirms the saddles fit, but the hair is weak and begins to break off by Jan-Feb).
i have always taken it off and not had a problem, but new horse has got rub marks despite well fitting saddle, so am going to leave it on next time i clip.