How patient do you need to be when training a new employee before you give up and realise they don't have what it takes?

First, run through the training procedure yourself. You know what’s expected of the employee in their position, but you don’t always know for sure if those expectations come through in your training process. Going through it yourself from the perspective of a new hire can help. You might also enlist another employee’s feedback, to make sure any common questions or concerns are covered.

Once the new employee is present, give them a packet of the process flow, the procedure notes or whatever other physical reminders you want to use. You need notes to run your training properly, making sure you don’t skip anything. Giving your new employee a copy of those notes will let them study in their off hours. It also gives them a resource to check before they have to come ask you for clarification

So must be very Patient 

Training a new staff means giving the individual a person to talk about himself or herself so that you can learn about the person more before you start with mandatory trainings.  It is important for a supervisor or manager to give the person a chance and a second one too because no-one is perfect in this world.  Everyday one is learning new things and achieving them step by step.  a member of staff never gives up on a person being trained to do tomorrow job.  there are two days in training for new employees and there are mandatory units to do online to learn more on the job.  Hence even if he or she takes abit longer at least he is able to deliver when they are made to work professionally and there is supervision which is an added factor for new employees.