90ma on a 1200mah battery isn't so much of a load that it would be dragging the battery voltage down too far due to excessive load, so I think that rules that out 1200 / 90 = 13 and I don't think C/13 is too high, especial for Li-ion which is widely used in high-output applications.
You're going to see a decline in voltage over time -- that's the discharge curve of a battery, output voltage reflects battery state of charge. With Li-ion batteries there is a relatively fast initial drop, then the voltage stays somewhat flat, then there is a rapid drop. I forget the range of voltages, but it's about a 30% total drop in output voltage from "full" to "empty".
My recollection of Li-ion chemistry is that they are a 3.65v per cell technology. So, a 9v nominal battery would be three cells for a total of 10.95v at full charge. If you're charging to less than that, you have less capacity, and if you've got an older battery, or one exposed to high heat, you again have less capacity. And finally, they age faster that other technologies.
What's the application?