I have an LG microwave that recently began shutting down after 6 or 7 seconds. I realized that it was briefly losing power and then turning on again, it doesn't continue cooking though. I tried using a different outlet but same result. This problem is the microwave then, not my outlet. Just wondering if this sounds like an easy fix or is the microwave needing to be replaced. I bought it in 2013 and is no longer under warranty.

It sounds like an overload is opening due to overheating. It could be caused by a fan not working or dirt. Attached are some manuals: https://dl.dropboxusercontent.com/u/8010163/Electronics%20and%20Electrical%20Troubleshooting%2 0and%20Repair%20Handbook.pdf
https://dl.dropboxusercontent.com/u/8010163/Electrical%20Theory%20and%20Diagnosis%20of%20Major %20Appliances%20Service%20Manual.pdf
https://dl.dropboxusercontent.com/u/8010163/LG%20Microwave.pdf
https://dl.dropboxusercontent.com/u/8010163/GE%20Microwave.pdf
Make sure to use your meter to diagnose whether parts are bad and follow all safety precautions.

" it was briefly losing power" how did you determine this?

I determined that it was losing power by watching the display. If I were to set the timer for 30 seconds it would stay on for about 7 seconds then shut off. I saw that the display went completely dark at this point and then reappeared. The clock was not set previous to this so I cannot say that it caused a complete reset but cooking was stopped after 7 seconds. I used a few different power outlets and the same thing happened at all of them. After speaking with someone at home depot (granted he was trying to sell us a new microwave) he said that it was likely the circuit board had been corroded due to steam (this is an over the stove microwave}.

Why don't you pull out the circuit board and fix it ?