My 99 expedition won't stay out of all wheel drive I changed the transfer case motor and now it stays I awd for about 10 minute then kicks back out and then the 4x4 light flashes and then it is ok until you shut the vehicle of and after you start it it will do everything all over again

The 4X4 system on your vehicle is computer controlled , GEM module . generic electronic module . The four wheel drive mode switch is a low voltage input to the GEM module . The GEM energizes relay's to control the mode as depicted by input from the mode switch an torque on demand relay an someother inputs . Probably has DTC - diagnostic trouble codes stored in the GEM module .
Transfer Case -Automatic Four-Wheel Drive (A4WD) The automatic 4-wheel drive transfer case system consists of the following:

• automatic 4WD indicator light
• brake pedal position (BPP) switch
• torque on demand (TOD) relay
• front output shaft speed sensor
• generic electronic module (GEM)
• 4WD high indicator light
• 4WD low indicator light
• 4WD mode switch
• rear output shaft speed sensor
• shift position sensor
• throttle position output (TPO) from the powertrain control module (PCM)
• transmission range sensor P1804 Transmission 4-Wheel Drive High Indicator Circuit Failure GEM REFER to Section 413-01 . P1806 Transmission 4-Wheel Drive High Indicator Short Circuit to Battery GEM REFER to Section 413-01 . P1812 Transmission 4-Wheel Drive Mode Select Circuit Failure GEM REFER to the Symptom Chart. P1815 Transmission 4-Wheel Drive Mode Select Short Circuit to Ground GEM GO to Pinpoint Test C . P1820 Transmission Transfer Case Clockwise Shift Relay Coil Circuit Failure GEM GO to Pinpoint Test B . P1822 Transmission Transfer Case Clockwise Shift Relay Coil Short Circuit to Battery GEM GO to Pinpoint Test B . P1824 Transmission 4-Wheel Drive Clutch Relay Circuit Failure GEM GO to Pinpoint Test A . P1826 Transmission 4-Wheel Drive Low Clutch Relay Circuit to Battery GEM GO to Pinpoint Test A . P1828 Transmission Transfer Case Counter Clockwise Shift Relay Coil Circuit Failure GEM GO to Pinpoint Test B . P1830 Transmission Transfer Case Counter Clockwise Shift Relay Coil Short Circuit to Battery GEM GO to Pinpoint Test B . P1836 Transmission Transfer Case Front Shaft Speed Sensor Circuit Failure GEM GO to Pinpoint Test A . P1837 Transmission Transfer Case Rear Shaft Speed Sensor Circuit Failure GEM GO to Pinpoint Test A . P1838 Transmission Transfer Case Shift Motor Circuit Failure GEM REFER to the Symptom Chart. P1846 Transmission Transfer Case Contact Plate 'A' Circuit Failure GEM REFER to the Symptom Chart. P1850 Transmission Transfer Case Contact Plate 'B' Circuit Failure GEM REFER to the Symptom Chart. P1854 Transmission Transfer Case Contact Plate 'C' Circuit Failure GEM REFER to the Symptom Chart. P1858 Transmission Transfer Case Contact Plate 'D' Circuit Failure GEM REFER to the Symptom Chart. P1866 Transmission Transfer Case System Concern - Servicing Required GEM REFER to the Symptom Chart. P1867 Transmission Transfer Case Contact Plate General Circuit Failure GEM REFER to the Symptom Chart. P1874 Transmission Automatic Hall Effect Sensor Power Circuit Failure GEM GO to Pinpoint Test A . P1875 Transmission Automatic Hall Effect Sensor Power Circuit Short to Battery GEM REFER to the Symptom Chart. P1891 Transmission Transfer Case Contact Plate Ground Return Open Circuit GEM REFER to the Symptom Chart. P1892 Trans. Automatic 4-Wheel Drive 4X4 Mechanical Lock Output Circuit Failure GEM GO to Pinpoint Test B . P1893 Trans. Auto. 4-Wheel Drive 4X4 Mechanical Lock Output Short to Battery GEM GO to Pinpoint Test B .
• Your best bet , take it to a qualified repair shop .