Monitor 2400 heater will shut down when I run My generator

More specifically, what all do you have hooked up to it?

try runnig it not hooked up to anything if runs OK gen is to small for your application

It sounds like you have a fuel problem, check to see if there is some kind of blockage in the line or at the tank value.

UU is generator under voltage. Check to see if it does it without laod also. if it does you will need a pro to check and ohm the rotor and stator for shorts

Since you had a power outage, you possibly have a circuit board issue. Try unplugging the heater for a couple of minutes then plugging it back in. If that doesn't help then a new circuit board may be needed. There are 2 different circuit boards. One main circuit board and one for the display. I hate to inform you of this but this are both very expensive. The main board will cost somewhere around $400. I'm not sure of the cost of the display board. If you have someone replace them, have them do to one and see if it fixes it. If it doesn't, put the old one back and replace the other, that way you can narrow it down to 1 or the other. There is a place in Ashville, NC that will repair monitor circuit boards. http://www.mathiselectronics.com/product-services/Monitor-heater.html Go to this link and it will give you prices for the repairs. They guarantee their work for 3 years. If you contact them mention you heard about them from Niten's Heater Service. Sorry I can't be more helpful.

Some manufacturers tend to fudge the numbers and throw around the 'peak' output power as continuous and it isn't. Peak (or surge) is the power a generator will handle as starting current (for example) for a motor and can be 120-140% of the actual continuous power.
Check you owner's manual, find the detailed specs which will normally contain the maximum continuous current rating. If it is listed separately for 120 and 220 (240) volts look for separate current ratings for each output.
By multiplying the current(s) times the output voltages you can find the total resistive output into a purely resistive load such as an electric heater.
For example: 120VAC X 20 A=2400 watts. If other outputs are available such as 220VAC, multiply its current rating: 10A. or 2200 watts Adding those two results 2400 2200=4600 watts will give you the rated power of a unit.
You can also recognize stupid power claims if the engine's horsepower is given. One (US) HP = ~746 watts. Since no generator is 100% efficient, its a fair rule of thumb to guesstimate the available electrical power at ~70% of the engine's rating (although, this is often also wildly optimistic). 10 HP X .7= ~746 X 7 or a bit over 5,000 watts.

It could be a dirty fuel filter or the small strainer located inside of the heater that is restricting the fuel flow. The problem could also be with the flame rod being dirty or touching the burner ring.

Is the amber light flashing on the monitor?

If so, you should get your power supply checked.

this might be overly technical, but it sounds like the video card is on the blink (no pun intended). I'd power down the machine, open it up, pull the video card, re-seat it, and power the computer back on.
If it continues to do this, that card is probably toast.