Pilot wont stay lit on my furnace

You would smell the gas, so you're probably ok. Lighting the pilot is not too tough, first you have to get the cover off the furnace. Inside you will see pipes and parts. Hopefully on the cover, inside or out, or somewhere inside the furnace will be instructions.
If not, find a knob that has 'pilot', 'off' and 'run' or something like that. It will probably be in 'run'.
Usually, you have to push the knob down and turn it to get it to the 'pilot' spot. When you do, have something to lite the pilot, which will be inside the furnace more, near the burner. The burner looks like a gas stove or oven burner. The pilot place will be at the end of a small tube.
With the button held down, wave something burning around the burner area. especially at what may be the pilot. The pilot doesn't put out much gas, so don't worry about things blowing up.
Once the pilot has lit, hold the button down for a while, at least a minute. Then you should be able to release the button and the pilot should stay on. If it doesn't, you need a serviceman to come. Let the landlord know the pilot would not stay lit.
If the pilot stays lit, move the knob to 'run' or such, and the furnace should lite, if the thermostat is set higher than room temp. If it has been off, and the room is cool, it should lite.
If the furnace doesn't come on, let the landlord know.
Most landlords have service people for this, it was my job for a long time. Lighting pilots was a common chore for me. If you can, have the landlord send one out to show you how to do it.
As you see, it's not all tough, but it's not all easy, either.

Replace the gas valve or thermocoupler.

check how many millivolts the pilot is generating. if pilot stay lit and burners wont fire u have a problem with one of the safties, lose wire connection, tstat control

this sounds strangely like a safety switch problem , ill bet the device that confirms the pilot lite lit before going to main burner has a problem

There is a window directly above the gas control valve. Either a spring held latch or a screw off cover need to be removed to access the pilot. To light the pilot, turn the knob to pilot and hold down while lighting pilot. The pilot in straight back inside the hole about 10 inches. Use a long fireplace match or rig a wire to hold the match. Once the pilot lights, hold the control knob down for about 30 secs., if it stays lit after release, turn to "On" and operate normally.

sounds like your thermacouplar is going out and needs replaced. Sometimes these will act like they are working fine , but when the pilot stays on for awhile and later goes out it is a sure sign that it is bad

It sounds like a thermocouple has gone bad. this is a very common problem with gas powered things ie; water heaters, furnaces, hot tubs. The telltale sign is when you release the pilot light button it won't stay lit. This is a safety feature and is relatively inexpensive and easy to repair.

it might be the hot surface ignitor. a common problem with gas furnaces also. also, check if there is an code on your screen. it will be called an FL code. call the manufacturer.

I'm a little confused by your terminology. You are saying you have a pilot lite and electric heat strips? Are you possibly meaning burners? Is the heater running for 2 hours straight without shutting off? how cold is it there? Lastly what temperature do you have the thermostat set at and how close does it get to the temp. before it shuts off?