That limit (290 kJ/kg (body fat)/day or roughly 31.5 kCal/lb (body fat)/day is given by this study
It works out to be a transaction limit of about 1% of your total account per day.
But you can also draw less energy from storage than that. If for example you don't need that much in a day ... obviously you will use less. Also there can be structural reasons that you can't access some body fat, for example if the tissue grew faster than it's blood supply (in which case it's probably hypoxic and very sick).
Finally one of insulin's primary roles is to push circulating energy into storage when insulin is high, and release it from storage when insulin is low. So if you can't get your insulin to go low when you need energy (ie: type 2 diabetic) then that will be a further restriction on how much energy from storage you have access to.
The underlying data from that Alpert study was from Ancel Keye's starvation studies after WWII. Unfortunately Seymore S Alpert died in 2014 so we can't ask him if there is other starvation data that supports or challenges his numbers ... but I am on the look out for starvation studies that could do just that.