Battery Drain

have a look:

http://www.fujifilmusa.com/support/ServiceSupportProductContent.do?dbid=687419&prodcat=616757&sscucatid=664277

I suggest using XD cards. Depending on the age of your camera there may be a factory fix available to improve this issue, you'll have to contact the Fuji repair center.

The manual states there is some small constant drain by design but 70mA seems high. There is no internal battery to retain the date, but with 2+ hours of the batteries inserted (or power supply attached) it is supposed to retain data/time for up to 24 hours (internal capacitance holds it). If you have a CF draining that will probably use all of the stored energy up though causing the date/time to be lost. Try it with the CF pulled out if that is the memory you are using.

Plugging in the adapter will cause a power-interrupt according to the manual. Be sure the camera is off when plugging or removign the supply.

FWIW I have switched to Duracell pre-charged NiMH hybrid cells in my S7000 and the "shelf-life" is much better than typical NiMH, took hundreds of test shots and views over a period of a week and there was still plenty of life in the cells. (They are rebranded Sanyo "enerloop" cells, google them up for more info).