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Shin-seiki: (002~004) This crap about the Eva being able to run at full power off the battery for only one minute is set forth here, only to be disregarded just about every time it comes up later in the series. That is, the Evas, for all practical purposes, have a five minute operating margin, not just one minute (see, for example, #25').
Dr. Nick: My guess is that "full power" mode is only needed when the Evas need to perform really insane athletic feats, such as jumping ridiculously high (episodes #08 and #09).
Reichu: EVA-02 manages to do that — and much more — in #25', while still retaining five minutes' worth of juice. Also, the three sprinting Evas in #12 were powered for five minutes. There's clearly something funny going on.
OMF: I doubt that—like the Eva's height—there is really any consistency with the charge on the internal batteries. They simply run out at whatever time the director feels would be the most dramatic.