Three AA batteries in series, only 1 depleted?
Simply put, one of your batteries is bad.  Or at least less good than the others.  In series, the current is the same through all cells.  So it is impossible for one cell to be drained faster than the others.  They are drained at exactly the same rate.  The problem is that one of the cells has less capacity than the others, so its voltage drops earlier.  

Putting cells of any kind (rechargeable or primary) in series demands that the cells be well matched or have some sort of balancing circuitry integrated into the pack.  

Basically, if you want to use multiple rechargeable AAs in series, they need to be the same brand, the same age, from the same pack, and should live and die together.  Charged together in series, depleted together in series, everything that happens to one cell happens to all the cells.  

And even then, sometimes you'll just have a bad cell.  

In this case, let's consider the current running through the cells in series.  

It will always be the same current through all three cells.  If one is significantly lower voltage, that means that the effective capacity of that cell is less than the others.  And, in this application, for all intents and purposes, the capacity of the batteries is going to be the capacity of the weakest link in the chain, as the voltage drops too far otherwise. 

How is it that one of the cells is delivering a lower capacity than the other two?  It could be any number of reasons.  Perhaps one is older, or has been used more.  Perhaps it is just a bad cell.  This can happen even when the batteries are new and all from the same pack.  It's not common, but it's also not exactly rare.  

It is absolutely vital that you use well-matched cells when in a series application like this.  Fortunately, I don't think the ESP8266 can drain the cells enough to cause a reversal of a bad cell, but it is something to think about:

Let's say you are discharging 4 cells in series, and one of them has lost some of its capacity, for whatever reason.  The current will be the same through all the cells at all times.  But, your device is able to run off the voltage produced even by just 3 cells working and 1 cell totally dead.  

What happens?  

Well, the bad cell is going to be discharged below the minimum voltage it should be, further and further, all the way down to 0V.  If you measured the cells, there would be 0V across this cell.  However, since your device can keep running even with a dead cell, it continues drawing current.  At this point, current is actually going to be forced through the dead cell, but in the wrong direction (discharging).  This is cell reversal.  In low discharge rate applications, it usually damages or destroys the cell prematurely.  In high discharge rate applications, it can cause the bad cell to vent (explode).  

Just be wary about batteries in series - you can't just mix and match rechargeable AAs in series, if that's what you're doing.