11spd Di2 batteries are rated for 500-600 miles operating duration. Unless your tandem is a garage queen, a year is unlikely on one charge.
Di2 battery life depends on the shifters, battery pack, weather, and the amount of shifting (esp the front derailleur).
We use the Ultegra 6870 (11sp) Di2 shifters and derailleurs. The older 6770 (10sp) shifters and derailleurs are bigger and apparently use more power.
We use the SM-BTR2 internal battery rated at 500mAh. This battery uses E-Tube wiring and is therefore incompatible with 6770 shifters and derailleurs. The BTR2 weighs 60g and is rated for 1,200 miles between charges. Since we ride in mild weather and out of the city (ie. less shifting), we can go farther between charges.
For tandems using the external SM-BTR1, the rated battery life drops by half to 600 miles. Although it's slightly heavier than the internal battery, the BTR1 has less capacity because the protective case takes up a lot of weight.
For most riders, Di2 battery life is a minor concern because its conservatively rated. It's convenient and easy to charge the batteries, and 1-2 charges should be enough for one season.