I have run an E36 M3 low before cause it started burning oil and forgot to check regularly. it would get a rough idle and once topped off, smoothed out.
An E9x should never get there because the level sensor should fire a low level warning so I suspect the sending unit may be bad. That plays more than the incline IMO because they were probably dry already and would likely have shaken on flat ground very soon too.
Suggestions would be to get your level sensor replaced and maybe take a peek through the filler cap once a month to make sure the system looks wet.