Automatik trans speed works some times, the engine is ok

is REVERSE OK
is PRNDL ( is L okay)???

OK what is the correct order to test. for sure not that
the service manual covers that, for sure the TCM.
1: ;all fuses good ,every one.
2: next is scan the PCM why skip such a key step> here??????
what if speed sensors fail.?
what if load modulater fail in the box.
the transmission book there and ATSG books tell you that and tells you that pump pressure test ports must be at spec or upshifts fail.
if pressure is low (or vast reasons) it can not fully operater the 2nd gear Servo piston to do so,

see my crude drawing her. (older tech box but works same in principle.
do you know what Limphome means for engine and trans?
on the trans, the TCM brain see horrible errors ,(you ignore)
and goes to limphome mode on the box. just 1 year or 2,
depends on actual box model like 4L60? GM box.there?
not sure I will look it up. not saying I know all Limp modes on all boxes.
below the shift lever is now a bank of shift solenoids
but they do the same thing.
if pump and its regulator work and filter not packed up or sucking air
the pump will have spec pressure at idle and the stall load test
the speed sensors must all work and no P07xx errors allowed
even some engine fail can set the trans to limphome too.
the FSM covers that (factory service manual)

ahhhhh you have this transmission same as my wifes GC2010
4 Door; 5-Speed Auto W5A580 Trans. aka NAG1, and 722.6
I have full manual books on it. but not your TCM
or it has this box
42RLE

learn to decode your VIN and see what trans is there first.

and scan it. next after fuses.
The scans see it all, engine and trans both.
and must never be ignored.

May be vehicle speed sensor. Any codes?

First of all, Hyundai Transmissions use a 'specific' fluid called 'SPIII' and ONLY SPIII. Any other fluid doesn't meet Hyundai's specification and can cause 4th gear slippage (which is the TTC - Torque Converter Clutch - frequently referred to as the "lock-up" converter). You should have had a Check Engine Light. The problem you describe regarding 'doesn't drop back to first when I'm at a stop' sounds like the transmission has gone into 'Fail-Safe' mode because of the 4th gear ration incorrect. In "Fail-Safe" mode, the trans stays in 3rd gear until you cycle the ignition key off, and then back on. You need to scan your engine's computer to see what/which trouble codes have been set/stored in it. You'll need an OBDII scanner to read any codes that might be there. When a 'check engine light' (MIL=Malfunction Indicator Lamp) is turned on, there is a DTC (Diagnostic Trouble Code) set/stored in the ECM/PCM (Engine Control Module/Powertrain Control Module). This code identifies which engine management system component/function experienced a malfunction. Once you pull/read this/these code(s), you can begin diagnosis.

have you done a trans service sometimes the filter gets clogged [its just a little screen in the trans housing] any leaks? perhaps torque converter is faulty you should have pressures checked but if engine is strong its likely trans problems do trans service first check fluid if it smells burnt replace it

U have an ignition related problem, have the system tested for the trouble code that is stored in memory any time the check engine light comes on to determine what is causing this issue. check engine lights have nothing to do with oil level or pressure, they indicate electronic control problems with the engine, trans or emission system.

Hello;
You may have two problems at the same time. The speed sensor is the easiest to replace. I would check and or replace the sensor. Then if the test drive shows the lock up fluctuating, I would replace the lock up switch in the transmission. Let me know if you have questions. Hope this helps. Rate me highly, please.
Thanks;
Rich
RPM Northwest

You need to check line pressure on the transmission. It sounds like a bad pump. Does it do the same thing in reverse?

Replace the speed sensor on the trans that will cause exactly what you describe is happening.

Check for trans codes then I would suggest a fluid change if there are no trouble codes, many times these kinds of problems are caused by a little piece of dirt causing a shift solenoid to stick.