I'm going to take a wild guess that the previous home owner put the blanks up because they had the same problem and didn't want to fix it. You likely have a short circuit and need to track down where the short is occurring. I'd remove the bulb from the fixture, unhook each of the wires that you connected before, and use a multimeter to test for "continuity" between the wires on each run (e.g. hot to neutral, hot to ground, neutral to ground for the line to the switch, for the light fixture without a bulb, and anywhere else that was previously disconnected). If you don't have continuity with a simple low voltage tester, then the problem could be arcing that only occurs when 120V is applied. Either way, get this fixed before turning the breaker back on with this fixture wired.
One reason bulbs can burn out quickly is if the voltage applied to them is higher than the expected voltage (120V in The USA). Wiring problems and bad transformers can cause the voltage to be out of spec. Another reason is if there is a loose connection somewhere, and the light flickers (causing unnecessary heating/cooling cycles). A third reason is if the light is in a confined space, and overheats.
In order to check the line voltage, you will need to use a voltmeter. The Kill-A-Watt is a very safe product to use to check the line voltage. Note that you should try a few different outlets, since there are generally two different phases of power (not really phases, but opposite polarities, 180 degrees apart) going into a typical house, and you need to check both of them.
Identifying a bad connection is trickier. Generally, you would see flickering lights, but to be sure you would want to use an oscilloscope or spectrum analyzer (expensive equipment). Sometimes a bad switch will cause a short flicker when the light is turned on. Replacing the light switches with new high quality switches could help.
Finally, have you noticed that the bulbs go out more quickly in certain places? Are those places more confined, causing the bulbs to heat up more? If so, you need to use lower wattage lights (such as CFL, halogen, or less bright incandescents) so that the bulb is less hot.
LED lights, halogens, and CFLs are all more efficient than incandescent lights. For the same amount of light output, they use less electricity, and generate less waste heat (keeping them cooler). In order to check if they meet your needs, compare the light output (in lumens) to that of the bulbs you are currently using. Don't go by the "equivalent" rating (such as 60W equivalent).... The amount of heat generated is nearly proportional to the wattage of the bulb (generally between 10 and 25 W). Another thing to look at is the color temperature, as measured in Kelvins. More orange lights will be around 2700 K, while more blue (daylight) bulbs will be around 5000 K.
PS: Advertised bulb lifetimes are usually assuming use of perhaps four hours per day. So, a seven year bulb may only last a bit over a year if it is left turned on continuously.
Best Answer
Non-trivial solution, but I would look at running a wire up the wall to the ceiling and over to the beam and either hang a chandelier from the middle of the beam, or install track lighting on the beam. You can use moulding along the beam to cover up a wire there so nobody will notice it (I did that for my living room which is now my dining room). If you do it right, you will only need to cut & patch two small sections of the wall/ceiling - one directly above the existing box and one next to the beam.