How to patch "keyless entry" car keys?

From a layman point, Yes its a design flaw and yes the signals are boosted to unlock the cars from far far away. This is knows as Relay Station Attack(RSA). Some of the ways to mitigate such attacks are:

• measuring Group delay time to detect illegal high values
• measuring Third-order intercept point to detect illegal Intermodulation products
• measuring Field strength of the Electric field
• measuring response time of 125 kHz LC circuit
• using a more complex Modulation (i.e. Quadrature amplitude modulation) which can't be demodulated and modulated by a simple relay station
• putting a physical on/off switch on the key

I don't think these mitigations can be used by the car owner themselves as there is quite technical detail behind it.

Taken from wikipedia. Smart keys and Security requirements

I have a car with such a keyless entry system. My dad saw a report about those ADAC findings on TV and he had an idea which works:

By placing the key in a steel can like the one above, the car does not detect the key any longer, so I figure range extenders would not pick up the key's signal either. Of course, this is annoying as it defeats the whole purpose of not having to take they key out of my backpack when I want to open the car and drive. But I guess this is still better than coming back to where I left the car, only to find it gone.

If you truly fear an RFID proximity relay attack, such that you would keep the key fob in a Faraday cage in your pocket, you must recognize that you will be giving up all the convenience of proximity, plus other inconveniences. You'll have to carry some kind of larger container, and you'll have to open it to take out the key to use the remote or the key.

I see two clear alternatives. If you are willing to give up proximity but don't want to sacrifice the other conveniences, there is a much cleaner solution than a band-aid tin in your pocket: disable the proximity system in your vehicle. That way, no external attacker can attack the fob in your pocket. You retain the convenience of being able to use the normal RF functions to lock and unlock the doors with the buttons. Check your owner's manual for instructions.

The other option is to pass the risk to a third party: buy theft insurance, and don't worry if someone attacks the proximity system; hooks up a tow truck; smashes your window; or any of the many other attack vectors. You give up no convenience, only money. And you're protected regardless of the form of theft.