same problem 3 times in 3 months with macbook air - power issue

I have a 2013 Macbook Air and it's running Yosemite. In February, i noticed a problem where in the middle of typing or using the Mac for something, the display would go to black for a few seconds then come back on.

Then one morning I went to use it and it wouldn't power on - no screen and no noise coming from the computer at all. When I plugged it in, the light on the charger initially wouldnt come on, but after plugging the charger into another macbook to check and make sure it wasnt an issue with the charger, it worked in thebother macbook and then the light would come on whenni plugged it back into my faulty macbook. I rang apple care and the over the phone support didn't work so I had to bring it to Belfast to the Apple Store. While there, the Apple genius couldn't figure out the source of the problem. He ran diagnostics on it and each piece of hardware came back okay - nothing to indicate the cause of why the machine still wouldn't power on. Eventually he just drained the whole battery and then when he plugged the charger in, it worked, the macbook came on and I was sent on my way.

The next month, exact same problem. Phone support didn't work and again I had to drive to Belfast. Again no diagnosis after running tests for hours on it. They gave me a new charger just in case, drained the battery and sent me on my way.

This morning I'm seeing the same problem again. I can't go to Belfast again as it's very expensive and also they don't do weekend appointments and I can't take time off. Has anyone any advice on what to do in this situation?

One thing of interest is this problem usually happens after it has been plugged in to the TV through a HDMI cable plugged in through an adaptor as I don't have a HDMI port.

Thanks!