Why is it that at night during the movie my light just suddenly goes off then it have to wait till it cools down to go again then it cuts out again.
But during the day it stays on for the full movie.

This could be due to the fluctuating voltage at different times of the day. If you feel confident doing it and wont kill yourself, it may be worth taking a few readings of your wall socket voltage at different times of the day to see if there are any significant changes.

Although, this could be possible I would imagine this occurring the other way around and that is fluctuations during the day compared to at night. Could it be possible that the socket you are plugging into could be tapped to another high wattage using appliance such as a washing machine, hair drier, microwave etc, that could have knocked out your pj when turned on? I had the same issue in an older house I rented when a vacuum cleaner was plugged opposite a wall that knocked out the lights within the kitchen when it was ran.

Yeah, thats seemed strange to me. Usually the voltage would drop in the day and go up at night.

i was doing some reading and the lamp holder said the suply wire must ba a minimum of 85 degrees so i checked the wire i use to plug in the light and it said 60 degrees could that be it?

I'd say that's unlikely. But you do want wiring rated for that temperature anyway. At least where it's exposed to high heat. Otherwise just ensure you're using the proper gauge wiring.

Is there some odd thermal fluctuation going on where you reside whereby it's cooler during the day and warmer at night??? At least where the projector is situated.

Describe your problem in more detail like how long does it take until the bulb shuts off. How long until it cools. What components are you using. Got any pictures of your build?

1. Do you by any chance have a thermal cut-off? If you have an eballast does it have a thermal cut of? perhaps heating / cooling is kicking in during the evening causing issues?. Perhaps the thermal cut off is faulty.

2. Try checking the connections. You might even want to open the wall plate. Thermal expansion can make or break a bad connection. I doubt it is the source of your problem, but it's easily checked

3. Test your line for current issues. Even if you identify the source of the issue you haven't yet identified the cause of the problem.

4. Isolate your ballast / light engine and plug it into a different circuit

5. A heavily loaded circuit, or ones with motors (spike at start up), heaters, or circuits with unusually long lines and thin gauge wiring, can cause localized current to flux or drop. Turn off other power sources on the line or try and isolate your projector on a little used circuit, and avoid using a long or thin gauge extension.

6. When I lived in California I noticed how crappy the line supply was. As demand changed during the day they brought generators on and off line causing spikes and minor brown outs. Local circuit configuration / load only compounds this problem. Many times these issues work together to make isolating the problem difficult. The answer to this one is more involved. Doing step 5 might be enough to minimize or over-come the symptom but not the problem. A UPS designed to filter the power might be an acceptable fix but costs money.

7. Get a good electrician to isolate your problem and suggest solutions. My brother is a master electrician and this sounds suspiciously like some of the problems he has run into. (usually long lines thin wires and heavy spiking loads)