Plastic cage around LED GU10 socket

Your G8s are probably 120VAC, right ? As such, you are not going to replace with LED without switching to LOW DC voltage. Most are 24V.

If you want dimmable LED (a good feature), you'll need a dimmable constant current driver and a magnetic transformer and a magnetic rated dimmer. You can use a standard dimmer, but the current surge will burn it out. (ask me why I know...)

Bottom line.. rip out the sockets.

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.