Your YashicaMat was designed to use a 1.35v mercury battery that is no longer available. The 1.5v alkaline battery you used not only has higher voltage (which can effect the light reading) but also a different discharge curve that can make the light reading change over time. Some users have said the difference is significant, others have said it wasn't an issue.
There are adapters you can purchase or make that will allow you to use readily available silver oxide batteries. Lots of info at
http://www.butkus.org/chinon/camera_batteries.htm.
Here are instructions for making your own adapater;
http://olympus.dementia.org/Hardware/PDFs/batt-adapt-US.pdf. I have one and it works fine in my Rollei.
However, none of this explains why your meter stopped working a few hours later. The .15v difference should not have hurt the meter circuit. My best guess is that the battery was old and at end-of-life. I would also check the battery contacts.
By the way, as to the "dead on correct" when compared to another meter, unless you ran a test against an evenly lit wall that filled the field of view of the meter, it's hard to really know. It's easy to find a 1/2 to 1 stop difference in two meters just as a result of differing fields of view.
The important thing is that the meter gives you a "close enough" average, allowing you to evaluate and adjust.