Two possibilities- - - -either the throttle pressure is too low, or the bands need adjusting. Since it shifts OK manually, I suspect throttle pressure. Look for some mechanical linkage that moves the small lever on the side cover of the transmission as the carburetor linkage moves, and adjust it so it moves further as the throttle opens. Make very small adjustments, as a little change in linkage length makes a big difference in shift points. There are some special fixtures involved in band adjusting, and one of the adjustment procedures involves dropping the pan, so try the throttle pressure fix first.
The most common slippage happens on the 2-3 shift, as the 1-2 shift usually happens at no more than 5 MPH in most cases. The truck will hardly be above walking speed when the first shift happens, unless you're at or near full throttle. The super-low ratio 1st. gear makes up for the fact the fluid coupling does not multiply torque for breakaway from a stop.
Jerry