Flash will not stay set

Yes, but not in the Auto mode, where the camera decides whether or not it needs the flash. Switch to the P mode, which works like Auto except you have control over the flash, exposure, and other factors. See pages 26 and 42 of this manual.

First make sure you're on Auto mode (press SCENE and choose AUTO mode)
Use permanent flash by pressing UP until the flash logo gets selected, then press OK.
Also, if you don't want to use the flash, put the flash on AUTO and press menu, go to "Set up", scroll to "Anti-shake AE" and set it to "Auto", press OK to save settings and try taking pictures again.

The flash settings don't work in some modes...what mode do you have the camera set to?

Maybe you have the ISO set to a very high number. Set it to "auto ISO".

In auto If it does not fire the flash bulb or flash board in camera will need service. In auto it will fire all the time as a fill flash.

In all of modes you can use "up" key to toggle between "always on", "auto"  and "off" mode for flash. (in some mode there is only auto and off.) also the flash light icon on top right of screen shows th status of flash. I hope this helps...

has the camera been in any cold weather or hot conditionds in a car?

the camera deffintly has a fault it has nothing to do with the settings any more

could be due to wearther conditions.

do u have warrenty this item? it will have to be professinally looked at i searched the web and its saying there is a seprate chip inside the camera that produces the flash unit ,and if you had to pay to get it fixed roughly 65 dollars

yes, the flash of your camera is not charging. needs repair.

it seems that the shutter of your camera is having a problem with. normally whin it gets stucked fully open it creats such problem. you need a help of a repairer.

Read the photo data (EXIF) and confirm what setting the flash was in. It may have been set to off by mistake. For close indoor shots I usually don't depend on the Auto setting, just manually force the flash on to get proper lighting. If you use the Auto setting take into consideration the white balance and the type of indoor lighting you are using.