Rechargeable battery Charging another device calculation
There are at least two key factors reducing the effectiveness of the battery-driven charger:


Tablets, mobile phones and other devices that charge via USB cables, typically contain an internal switching regulator as part of the inbuilt charging controller: My HTC Desire phone's battery indicates 4.07 Volts at full charge, and the charging pin shows 5.2 volts, higher than the incoming USB voltage, so there's a boost regulator in there somewhere. Assuming 85% efficiency in each boost regulator (inside the tablet, and in the charger), combined efficiency is 0.85 x 0.85 = 0.7225 or 72.25%. Actual efficiency is likely to be quite a bit lower.
Unless the tablet is charged while fully powered down, it's own operation will be consuming a fair part of the total power delivered from the charger, thus both increasing charge time, and massively reducing actual charge delivery to the battery - most of the power ends up as operational and thermal losses in everything from the processor to the screen backlight, the radios for WiFi, Bluetooth, and perhaps mobile connectivity.


Observations on my various phones and other devices indicate that they go from a power-efficient mode to high performance mode (processor runs faster, screen brightens up) as soon as the charger is connected. While this could perhaps be prevented through power management changes in the device, the default behavior is power-hungry while charging. 

For sizing a battery powered charger suitable for charging a mobile device, I would suggest a factor of at least 2, preferably more, in the mAh rating of charger compared to the target device. 



Update: Power estimations, assuming [Eneloop HR-3UTGA][1] NiMH rechargable AA cells.

Tablet requires: 3600 mAh
Assumed efficiency: 85% (for each of the two boost converters)
Need from 2xAA: 3600 / (0.85 x 0.85) = 4983 mAh (to charge if tablet powered off)


Working the calculations the other way around:

Available, 2xAA: 3600 mAh (assuming around 1.5 Amperes drawn per battery)
    (Discharge graph in datasheet, between 1 and 2 A)
Delivered to tablet: 3600 x 0.85 x 0.85 = 2601 mAh (after tablet's boost converter)


Thus, clearly the 2xAA charger will not have sufficient power to fully charge the tablet, even when the tablet is powered off.

While it is not feasible to estimate power consumed by the tablet during operation, a totally "sounds like a good guess" assumption is in the vicinity of half to two-thirds of available power feed.

Thus the tablet should be expected to charge up to between 858 and 1300 mAh worth, before the AA cells in the charger are depleted. The observed figure is around that figure, so nothing significantly amiss in the behavior described in the question.