For an upcoming ESP8266 project, I need to use a relatively large (or several smaller) batteries and am hoping to get at least 10Ah. To achieve long life, I will be utilizing one of the ESP8266's available sleep modes. In the deep sleep mode, it utilizes somewhere between 10 and 70 microamps.
I know that most lithium ion batteries are recommended to discontinue discharge at a voltage of around 3.0-3.2V, for the sake of battery health. However, do they also have any kind of limitation such that the battery will not supply current if the load goes below, say, 1mA? I apologize if this is a nonsensical question, but I know very little about batteries, and I want to ensure I can put it into deep sleep while using a battery like this.