Hi. Most likely it`ll be worn or near worn out motor brushes even though you say the machine does spin. What often happens is that although the brushes are worn out there is a short period of time where the electricity jumps through the remaining brush and so the machine can still sort of work but not for very long. These, and most other machines, are wired through the motor so if there is a fault with the brushes the machine eventually even fails to do anything ( other than the facia lights remain on ).
There are 8 versions of a JLWM1203 and parts are based on the product code, begins with 91??????/??, and not the model number Jlwm1203 ( John Lewis machines are really re-badged Electrolux / Zanussi machines, well, for our purposes they are ) the trouble is when you look up on say, the Zanussi site you will find only an expensive motor listed and not the motor brushes and that really is due to several different motors that are used ( brought in parts ). The most common type of brushes on your model used are Ce-set the other being Sole brushes ( and they will look completely different ) but neither of which will inter change and so you will have to match your brushes up to pictures which should get you the right ones. It is important that you note the angle of the actual carbon bit end of the brush, does it angle to the right or angle to the left? – Ce-set brushes are used by every manufacturer and man and his doggy in other words the plastic bits may outwardly look the same but they are not, same goes for Sole motors too.