Why does the measured potential-difference between two poles of an AA fizzle out after 5 seconds?
I am answering to counter some of the misinformation in the comment section. I don't have a good explanation for what is happening, and I have never seen something like that before. Normally, the voltage holds steady when the Voltmeter is connected. I suspect there is some problem with the probe or the voltmeter (although fluke is a very good brand) or the test setup. Maybe you are making intermittent contact because you are not pushing hard enough.

But for an alkaline battery, if the open circuit voltage is at 1.3V, the battery has little or no life left in it. If you discharge an alkaline battery under load until it reaches 1V or 0.9V, then remove the load, it can easily rebound to 1.3V. But as soon as you put the load back on it, it will go right back down to 1V or 0.9V. Personally, if I see anything under 1.4, I toss the cell. If it is close to 1.4, I consider it about half way used up. Fresh cells are between 1.5 and 1.6, usually.