It depends on the battery and the usage.
Lipo batteries can die, if there is a demand on the battery (some alarms), and the battery runs completely flat.
Lead acid should not be a problem, even if run flat, and it is most likely you have lead acid batteries.

If the battery is super light, it is probably Lipo. If it is f'in heavy, it is lead acid.
You can get trickle chargers (your existing charger might be a trickle charger) and you just leave these plugged in while you are away. Trickle chargers were designed to do this.
Most batteries if disconnected should hold the charge for at least 6 months. I have powertools with Lipo batteries that don't get used for months on end, no problems if there is no drain on the batts.

If you cannot get your ebike into your apartment, I suggest you at least haul the batteries upstairs. That way there is much less chance of your bike, or batts, being stolen.

There is loads of stuff on Google about this. If you have another kind of battery (unlikely) search online for info.