Our delonghi portable gas heater's flame will not stay light once we the ignite button is released?

First and foremost be very careful !
Multiple attempts to light a pilot with no ignition could cause a gas build-up and then ignite with a WHOOSH !!
Have you shut off the gas and electricity completely and then turned them back on, then tried to light the pilot light?
When trying to light the pilot light, do you get a flame but it won't stay on?
Systems I have seen require you to hold a switch/knob open while lighting the pilot light, and continue to hold once lit until the thermocoupler heats up (this keeps the pilot light going once you release the switch/knob).
If you are not getting any flame, have you verified that your gas is getting to the heater?
You don't say what cause the pilot light to go out. . .
Post an update if nothing above has helped you.

These are designed not to light once the thermocouple fails.the thermocouple has a small wire that positions in to the pilot light which checks the pilot is on and keeps the gas governed.once the temperature drops it shuts off the gas to prevent a build up of gas in a room where a pilot light has gone out.this is why you need to hold the button in on reignition to allow the thermocouple to heat up so the gas keeps open.
Try to relight by turning on the gas ....pressing down and holding the button for at least 10 seconds whilst firing the piezo to ignite flame.do not release gas button for at least 10 seconds then slowly release.if the flame on the pilot will not stay alight....then it is likely the thermo has failed.try cleaning the metal wire that is above the pilot jet.still no joy then it needs replacing.hope my comment is of help...please vote.

I'm sure that you read the directions and you are holding the button for a full minute.

1) Try blowing it out with a hair dryer. Dust does lots of weird things to gas heaters.

2) There is a thermocouple that opens when it is hot and makes the gas keep flowing. It is a small metal tube that sits directly in the flame. When it heats up, the gas flows. If that is shot, then it won't keep the gas flowing, so it will turn off when you let go of the button. Try tapping it lightly with the tip of a screwdriver to knock it loose. There is about a 10% chance that this might fix it temporarily until you can get a new one.

wile red button is pushed no flame or turns off when the button is released the flame dies ? if no flame tank is too small or spark isn't in far enough to catch gas . if flame is present with button down then the over heat switch on the in line thermal coupler could b bad u can check the over heat switch with a jumper between the two wires and if it stays lit you got it if it goes out then its the thermal coupler that's bad

I would start by replacing the thermocouple. It is suppose to keep the gas valve open when in operation. If the mercury in the thermocouple dries out it won't keep the gas valve open and thus the flame goes out. If that does not work then you have a gas valve problem.

Without a pilot flame sensor signal the pilot light will not stay on and the heater won't work. Try Replacing the pilot flame sensor, the pilot flame burns on to it and it connects to the valve. It looks like a wire.

Blocked pilot flame too small or thermocouple needs replacing

Does this unit have a thermocoupling?

If so replace it. (6 bucks)
It is the units flame sensor and they routinely go bad.
When they no longer sense flame the unit will shut off gas to the ignitor/burner.
It will only stay lit when you are manualy holding the button.

the little copper tube that sits in the pilot flame is faulty. this is called a flame sensor. replace this and you should have no problems