I don't know about your specific projector, but there are two common triggers in general. The first one is simply lamp hours. Did you reset the hour counter when you replaced the original lamp? If so, then the projector may just wait until the hour counter gets back up to a couple thousand hours. At some point, however, your lamp will no longer strike because the voltage is too high. This leads to the second possible trigger.
The second trigger is the lamp voltage, which varies with the arc gap. Once the voltage is too high then the ballast will no longer be able to maintain the arc, and it will go out or be unable to strike. The ballast can read the voltage and may be telling you that it is getting close to an unusable voltage. However, there is a special waveform that is run through the lamp to sharpen the electrodes to keep it from flickering and this can actually reduce the gap (and the voltage) in the short term, especially if you run it for long periods of time. This is why near the beginning of life you might actually see the image get slightly brighter than when it was new (A smaller arc means a brighter image). However, in the long term you will need a new lamp as the "macro" burn back will overcome any "micro" sharpening eventually.
You also run the danger of lamp explosion whenever you go beyond the recommended lamp life, as the glass envelope degrades over time. This failure has become less common as the materials and processes get better, but it still happens from time to time.