So sorry for the late reply! It's been a hectic time here at TWA and forum posts had taken a bit of a back seat to support tickets.
Are you changing all three batteries? Since it's powering down almost instantaneously or powering on just long enough to display a low power warning, it indicates that one of the three batteries is dead.
If the problem persists, shoot me an email at firstname.lastname@example.org
sorry to hear about your problem. If this turns out to be a Battery Problem as Nicholas Quitana suggests it might be, you may find it helpful to read his and my replies to Duane Woody's remarks in his Topic "Batteries".
I'm suggesting that you look there to save myself and Nicholas repeating what we've already said. I will however give you a tip which I didn't mention there, and which has helped me on one or two occasions.
In the Batteries thread I suggest Eneloop Rechargeables and "an intelligent charger". By that I mean a charger which controls each battery separately. I personally only use chargers from Panasonic (Eneloop belongs to Panasonic) and have two chargers. The one that I really like is the Panasonic BQ-CC55 which can take AA and AAA and indicates when a battery is defective.
Nicholas states that if a battery is defective (or "dead" as he puts it), you could possibly experience this phenomenon. Since I've been using Eneloops I've had no power issues with any of the devices running on Eneloops. His advice regarding always changing all of the batteries is good and does not only apply to the TWA. Using rechargeables means that it basically costs next to nothing to charge (and replace) a complete set when the unit shows "low battery".
I hope that this has been of some help.
I just remembered this video from Dave Arnold. Maybe this could be of some help.
You can find it under Community Forums/Tips and tricks/Tuesday Tips with Dave #1 - Battery powered preamps.
I hope that this may be helpful.