Sounds like a thermal issue to me!
Seeing that when an additional Lamp is run in the same fixture, one (or both) Lamps will fail very soon afterwards, points to an issue with ambient temperature.
To the OP:
Verify the Lamp Wattage does not exceed what is listed on the fixtures.
Have your Friend describe what is listed as maximum Lamp wattage, and what is being installed.
Try using two CFLs (Compact Fluorescent Lamps) in one Fixture, to see how long the Lamps run correctly + without noticable decay (hard starting, overheated bases, low light output, blackening at points on the tubes, etc.) or if the Lamps "Cycle" (turn on and off randomly).
Try this in the most problematic fixture.
Another test would be to install Incandescent Lamps with either lower wattage ratings, or higher voltage ratings - or both.
- If the Maximum Lamp Wattage rating for a certain fixture is "150 Watts" (maximum of two 75 Watt A17 Lamps), try using two 40 Watt Lamps. See how long they last, as compared to prior Lamp replacements.
- Try using Lamps rated at 130 VAC (Volts, Alternating Current) in the same fixture, with a combined Wattage not exceeding the fixture's rating.
- Try both "1" and "2" above in the same fixture - lower combined wattage and higher voltage rating.
These Fixtures likely do not include Thermal Protection, so instead of a Fire, the Lamps are "Comitting Suicide", in an attempt to reduce heat concentration.
As others have mentioned, how fast do the Lamps fail, are the Lamps the "Cheap-O" brand, are they + fixture sextremely hot when running, and is there any possibility for failures due to vibrations?
Lastly, verify running nominal voltages at the Fixtures during operation, and observe pecular Lamp operation due to Voltage sags and spikes.
If the Voltage at the Lamps is > 10% of the Lamp's rating, the drawn power (wattage) will be higher than what is rated - and results in higher heat + light output, with shorter life.
If Voltage is above rating & combined wattage exceeds the fixture's maximum, this will kill standard duty 120 VAC rated medium base Incandescent Lamps really fast.