Do electric car batteries lose their stored energy over time?

All batteries have a self-discharge rate. The rate varies by type of battery, age of battery, level of charge, and temperature. If you estimate a lithium ion battery at 2–5% per month, you can figure your car will start just fine after sitting 2 weeks – if there are no other current drains like alarm system, keep-alive circuitry, wifi, bluetooth, etc.

I concur with @LuckyGuy. Self discharge will eventually drain your battery. Even shut off most modern cars will have a trickle draw of current. The age/health of your battery will also factor into the eqn. Usually 2 weeks is not going to kill your battery.
If you shut off your phone and remove the battery it will hold charge for a very long time. I have a handfull of old phone batteries andvthey still had charge after a couple of years

The battery will discharge, but just as the battery started your car at the airport after 2 weeks, no manufacturer is going to field a car with a battery that will drain away in 2 weeks under no load.

Many new cars have fancy schmancy, and IMO useless, proximity keys. They are (supposedly) so convenient! All you need to do is walk up to the car with the fob in your pocket and, like a dog needing to go out, the car responds by unlocking the door, adjusting the seat and remembering your radio stations. Push the start button and go. Isn’t that convenient? But…

Think about how that system works. There’s a radio receiver and transmitter that are continuously listening for the key’s frequency and code. They wake up when the receiver senses a key with the right frequency then they interrogate it to check if the code is correct. They do this every time someone with a similar model key walks near your car. Eventually, usually in about a minute, they times out and goes back to sleep. If you drive a common vehicle and park in a really sweet parking space by the entrance, your car can be searching and interrogating all day long.

Wisely, some auto manufacturers allow you to turn the system off manually if you are parking for more than a couple of days. You need to read the manual.

Can you tell I dislike those systems.

I know someone who has a fancy newish corvette. Took a while for him to figure out why his battery kept dying on long weekends. He would place his key fob on a hook near the garage. It was in close proximity to the car and it would keep certain circuits awake and slowly drain power.

It may go dead if there is a slight drain. In the 12 volt automotive batteries, the battery can discharge through the case to ground, if not insulated further than a metal battery box. It can also drain if there is moisture on the battery, in contact with the terminals. But a large electric battery, such as those used is electric cars, if there is a slight nominal drain, wouldn’t be noticeable.
For those who might be interested in purchasing a electric car, consider the resale value of the car once the battery goes bad. (Battery replacements, I’ve heard, start at $10,000.)

Like people said above, two weeks should be no problem.

Even gas cars can be a concern about the battery draining over time.

Car batteries lose power over time naturally, also many modern cars draw from the battery to seek proximity keys, etc.

Some BMWs move the wipers slightly about every two weeks if not used in that time.

Dead batteries due to sitting is one of the things we call “lot rot” in the business. A good Inventory Manager at a dealership will check the stock for dead batteries. If one is found a jump box is used to start the car, then the car is idled for about 20 minutes to recharge the battery.

If your battery is going dead in two weeks you have (hopefully) a battery in need of replacement.

If not, something is causing an incorrect current draw and should be checked by a technician.