Li-Po battery cells have 4.1V when fully charged, 3.5 V when fully discharged. Now:
* Such cells will release hydrogen, swelling and damaging the cells; they do that very slowly when not fully charged, but the release rate can increase by two magnitudes when fully charged. That's why the battery IC (Battery Management System) will auto-discharge it to 60%, or circa 3.8 V.
* The cells will slowly discharge, due to their chemical balance, and due to the electronics requiring some miniscule current. So keeping the cells at 30% would really mean you have to check them each month. But keep them at 60%, and it will take over 3 months to self-discharge them - then you only need to recharge them once per season.
* When fully discharged, voltage of the battery will start to drop below 3.5V. If it drops to 3.1V per cell, nothing that bad should happen, the battery will take up to few hours to recover but will recover. But if it drops below 3 V, it might have effect on the chemical separation - the electrolyte, rather than keeping the electrodes stable, will start dissolving copper atoms and depositing them somewhere else. Depending on type of electrolyte, it may also crystalize or become thicker in parts of the cell. This will increase self-discharge current and the cell will drop voltage even faster.
* To avoid flying with damaged cells, the IC controlling the battery(Battery Management System) verifies its voltage. When it detects a cell has below 3V, the BMS will raise "Permanent Failure" flag. When this flag is raised, the BMS will no longer allow to charge or turn on the battery. Permanently.
* There are software ways to remove that PF flag, but if it was raised, then it is likely that the cells are damaged - they are probably still ok to use as power bank for your phone or other low-power tasks, but flying with such a battery can lead to sudden power drop or a fire. It is possible to re-charge and unlock a battery which cells went as low as 0.5V - but then, you've lost almost half of the battery capacity, and the self-discharge rate of such cells is so high that 3 months may be enough to drain it completely.
Also note that temperature is a factor. The battery will self-discharge slower and release the hydrogen slower in low temperatures. Unless in reaches 0 deg Celsius, then each time the electrolyte starts to solidify the battery will discharge a bit to get it back to fluid/gel state. So freezing temperatures for prolonged periods are bad (though the freezing point is really below 0, it depends on the specific electrolyte used).
The voltages I provided are for no load case. When under a load, the voltage drops.