In theory the purpose of the short drive after boosting your car should be to charge the battery via the alternator. If you cannot start the engine at all then the chances are that the battery is the problem or something unrelated and more severe. If from this point on your car drives fine and doesn't lose its charge again then this may have been a 'one off' problem and it may be that you simply accidentally left the lights on in your car, or maybe left the radio on too long. Cold weather can also sometimes be enough to 'freeze' the fuel cells in the battery and prevent them from working if you have an old car, while leaving the car for a long period of time without using it can also cause it to gradually lose charge.
However if the battery loses its charge again then this means either the battery has lost the charge faster than the alternator can charge it back up, or the alternator has failed to charge it as you've driven and it is hard to differentiate these two cases.
To do so, one quick method is to look through your car's service history and see how recently the battery was replaced – if it only just happened then this might suggest you have a damaged alternator or another problem. To inspect closer, open the bonnet and look at your battery and alternator. The battery will have a small lightning symbol on it and may have a plastic cover over it, while the alternator may be located behind the engine on a bracket. Consult your car manual if you are not certain where your car parts are located.
Now direct your attention to the connections between the alternator and the battery (with the engine off of course). You should also check the alternator belt for damage. Either of these can be the cause of your problem and may allow you to fix the problem yourself. In the former case this might suggest that the problem is not solely the battery or the alternator, but rather the conduit between the two.