How long does it take to recover from very low potassium level ?

I would guess hours or less.  Potassium salts are soluble, drink some electrolyte solutions, lie Gator-aide . . really low then the hospital will give you an IV.  ---  My guess is that you are being treated for high blood pressure by some quack who is giving you a high dose of diuretics to remove sodium from your system.  But you will also get rid of potassium at the same time,  ===  This happened to me and I passed out because of the low potassium level.  I quit taking the damn diuretic and my body adjusted by retaining potassium.  No other treatment and I recovered in about 48 hours on my own ===  and I quit going to that Quack. = = = I went to another doctor and he looked at the problem and immediately asked why the other doctor had not prescribed a potassium supplement with the strong diuretic (because they tell you that in Med school)

It depends.  Is the person still alive?  If not, it will take a very very long time.