Battery charger for AA batteries
From TagSense’s datasheet (and Matt’s comment), we can see it was designed for CR123 - non rechargeable battery. 


Also it can be seen the device can operate at 2.2V .
Regarding daily average consumption:
If 4 Batteries of 1550mAh operate the device for 12 months, this means 517mAh/month, or just 17mAh/day.
So it appears to me that any good AA NiMh would work. I have several Eneloop NiMh (1800mAh) and they are great, providing 1.30V when fully charged and around 1.20V along most of its discharging cycle, so 2.2V minimum voltage is fulfilled. 

I would try 2 AA Eneloop NiMh batteries. Brand-new and freshly charged, they would last about 3 months. If transmitting power and range would be OK for you, as TagSense will operate at lower voltages, then you could use a SMALL Solar Cell panel as energy source, as one with 

100mA &lt; capacity &lt; 200mA and 5V~12V rated, 


powering a low quiescent current voltage regulator adjusted to 2.60V to charge 2xAA NiMh in series. If solar cell is small, you wouldn’t need to worry about current limiting, otherwise is recommended to include a simple current limiting circuit. 

A suggestion of series regulator for this charging is based in the TL431 found everywhere, adapted from Texas’ TL431 datasheet, and paralleling common resistor values (5% series) to obtain desired voltage divider. When not charging the resistor divider drains only 100uA or 3mAh/day, so it is negligible for the charging currents. It is mostly a starting point, as other charging methods and charging figures would influence the circuit selection. 



Let us know which path you followed, ok?