1992 Geo Metro w/ automatic. In drive, won't

Your probably looking at a transmission rebuild. But it is sporadic. Could be a valve body problem or solenoids. and electrical. Throw it on a scanner and find out.

my guess is its not electric shifted, (what trans model is it)
so step 2 in the FSM book says.... and i paraphrase
step1 is stall test (my guess passes in 1st and reverse)
step 2, line pressure test?
if that fails, tranny is bad.

nice double post, backup one and see answer.

my guess is a bad governor.
bad throttle valve, on rear of tranny, either the cable one, or vacuum one.
the tests are all in the FSM and online at alldata.com, for $15

a/T trans,
does it fail to shift to 3rd with light throttle and flat ground moving say 45mph? Y/N.
trans diagnosis is complex , so is the trans.
it a hands on deal too, with tools.
1: is modulator valve working?
2: is Kickdown cable not stuck at WOT?
3: is filter screen clean?
4: is A/T pump pressure at spec.?
the car has an FSM and in this book , as a section called, on car repairs. for A/T . its 100% on topic.

is it slipping,?
if the rpms rise and car dont speed up , in direct proportions that is slip.
is it?
if the engine has full power in 1st, the the transmission is bad.

not sure what shift manually means,
Drive to low? low to high. what? be exact in statements/
better stated what it does good and bad, and when. all modes.
are you saying the trans shirts perfectly in AUTOMATIC when cold./?

It may be just the vehicle speed sensor. Does the speedometer work OK? The vehicle speed sensor tells the computer how to control the shifting and it also sends a signal to the speedometer. Is the trany full of fluid, is it fairly clean? It should be red. Most vehicles, you check the fluid with the engine idling, in park.

Auto Trans I had to replace solenoid in transmission there are two of them when you drop the pan. After testing with a 12 volt battery one was bad replaced and transmission works fine. Mine was a 1996, cost about $90 for solenoid.

The accelator cable is "Y" shaped. one side goes to the carb and the other to the tranmission. If you have the carb.side too tight it will give you the problem that you are having.
Robert