Li Ion battery issue (voltage appears and disappears)
The effect you see is the standard behavior of electronically protected battery when it reaches the protection over-discharge threshold. 

When you load and drain the battery in a device, the voltage of internal cell will gradually drop down. When it drops below the threshold imposed by protective electronics (typically 2.5 - 2.7 V), the electronics disconnect the cell from external electrodes, to prevent overdischarge. 

Now, the actual voltage on cell (internal) terminals depends on ESR and load current. When you disconnect your load, the cell voltage will instantly jump up by dV = ESR * Iload. The protection circuit usually has some hysteresis, so it won't immediately disengage, and the external battery terminals will be at zero output again. 

Then two scenarios can happen, (a) the cell has high self-discharge rate, so the output will remain at zero, until you put the battery into a charger, and (b) the cell might self-recover a little bit, after some time, so the internal no-load voltage becomes above the upper threshold of the protection circuit, and external terminals will show the voltage (~2.7V) again. Loading this discharged battery will result of a very short "working" time, then the voltage will again drop to zero, due to workings of battery protection. 

Obviously this behavior will have many timing variants depending on hysteresis levels of the protection circuit, current ESR of the cell, and load current.

You should disregard this marginal behavior at the verge of nearly-discharged cell. Electronics in your device/car should stop (disconnect) using batteries if their (external terminal) voltage drops below 3 V, and re-charge the batteries immediately.