If the car has keyless entry, it sounds like a keyless-entry theft, which are very common these days. There's lots of ways to prevent relay theft on keyless entry cars. The number one way is to stop the key being vulnerable by blocking the signal. Thieves use relay devices (which you can easily buy online) to amplify the signal from the keyfob in your home to a transmitter near your car, which essentially tricks your car into thinking the key is present. This allows the thieves to enter the car and drive away. Faraday bags are a good preventative measure, they work by blocking electromagnetic fields. This stops radio frequencies from being amplified, all you have to do is put your key in the little bag (www.amazon.co.uk/MONOJOY-Blocking-Antitheft-Protec...g)

However, there are also videos on YouTube that explain how to make your own Faraday Bag using materials around your house if you don't want to spend anything. A Disklok is also a good, physical product to prevent vehicle theft (review here: kit.honestjohn.co.uk/reviews/review-disklok-steeri.../).