My speedometer works initially when I start my territory and then after driving maybe 10-15 minutes and usually at higher speeds it just quits. What could be the problem?

its located on transfer case rear end near propeller shaft , have 3 wires plug

could be the VSS - vehicle speed sensor .
Speedometer and Odometer
The Vehicle Speed Sensor (VSS) is a gear driven permanent magnet generator. The vehicle transaxle houses the VSS. The VSS generates a sine wave output with a frequency proportional to the vehicle speed.
The Powertrain Control Module (PCM) converts the CKT 389 signal to an output that switches to ground at a frequency of 4000 pulses per mile. The CKT 389 signal drives the speedometer and the odometer. Various other vehicle components use the CKT 389 signal. Refer to Engine Controls.

YEP YOU NEED VSS SENSOR HOOKED UP SO TRANSMISSION CAN SHIFT RIGHT.AND SHIFT TO OVER DRIVE AT SET SPEED. YES YOU NEED TO SEE YOUR SPEED TO KEEP FROM GETTING A SPEED TICKET.DONT UNPLUG IT.

Sure you can if a mechanic can do it so can you if you have the right tools and knowlege. First you need to know which one thers's one at each whell at the fround rear end housingf the rear rear end housing and the one in the side of the transfer case where the speedometer cable would'of connected on an older model and then theors three in the sides of the trans mission, Touque converter speed forward turbine speed output turbine speed. What proble are you trying to fix? the speedometer not working? Abs light on? Cheack engine light on? Cruise control not working? If the cruise control does work the speed senser is good and the check engine light will be on if the speed senser is'nt working. If the speed senser is'nt working the car will only take off in low and not shift to seecond or any higher gear as the computer doesn't know how fast the car is going. If the speedometer is'nt working and it does shift and cruise and the check engine light is'nt on then the speed senser is working but the speedometer is'nt if it is'nt and everything else is woring then as your driving hit the speedometer with your fist and see if it comes back on they can get stuck and i've fixed quite a few and they stayed fixed. On to wheel drive models with the rear wheels jacked off the ground safty I've run the car up to speed and trying wiggleing the wires and connectors till I wiggled the right thing till the speedometer came on ( including smacking the speedometer ) Just don't hit it too hard as it'll bust just like anything else.

The transmission quit shifting, and the speedometer quit working.
When you say the transmission quit shifting, do you mean you backed out of your driveway, started driving down the street, no speedometer, and you just stayed in 1st as the engine RPM's got higher and higher ?
Please explain what has happened. You should also have a check engine light on in your dash. You will have to plug a OBD II reader in to pull any codes, so we can help you find the problem. Please let us know.

Speed sensor from the transmission. If speedometer doesn't see it,,,,neither can the cruise control

It maybe the speed sensor that sends the signal to the speedometer or the speedometer itself that's has a short in it.

first of all, the power steering pump doesn't stop working and then start working usually they are just bad. second of all it shouldn't take 3 hrs to change speed sensor, and last the vss could cause all symptoms, if the car has variable assist steering the speed sensor could effect this

U need to replace the vehicle speed sensor on the transmission, it has failed this will fix all the problems. see photo of sensor.

it's the cluster just the piece alone cost $680.00 plus tax