Well, stress and consequences aren't really designed to be a typical resource depletion mechanic, so you may be looking at a "square peg, round hole" situation.
Consequences don't seem intended to model something that happens repeatedly the same way. The consequence you take is generally supposed to be directly tied to the narrative that produced it, and if the narrative is always, "out of gas" that's kind of boring.
Also remember that mechanically, consequences don't typically outright *stop* the character from taking an action. They are Aspects that can make life difficult. So, if you have a consequences "Out of Magic Juice" that typically doesn't mean you *cannot* use magic, but that it may be more difficult if the opponent chooses to use the aspect against you.
Beyond that, the answer may depend upon the metaphysic of the magic system involved. Remember that the end result of taking stress and consequences is being "taken out" - meaning you cannot act in the scene at all. This goes well with a system in which use of magic can really burn the character out to exhaustion.
In which case, you can have a "mana" stress track, and just allow the character to take magic-related consequences if they run that stress track down. The consequences could be related to mana, magic, or just general fatigue to fit the narrative.
Note that consequences can last a while - If you deplete the resource enough to take a consequence, you may be out of mana for an entire session or even an entire story - at the upper end, this resource does not refresh quickly.