Every boss hires new employees with the thought that this could be a long-term working relationship. The boss is hoping this is the case, as is, in most cases, the employee. Both parties are willing to work through the rough spots, to get to that place where the employee is comfortable with the work and the boss is confident in the employee. Sometimes this takes longer than other times. Some employees need more training, a little more help to get them started working on their own. If their work is good and you are happy with their performance, this does not seem like such a big investment to you.
There are those employees who just never seem to catch on. You are beginning to think that this may not be the right job for them. You obviously hired this person because you felt they were good for your company. Maybe there is another position they are better suited for. Unfortunately when all avenues have been exhausted it may be time to terminate your relationship with that employee. It may just not have been a good fit. Obviously he or she is not the right person for the job. They may feel the same way. Maybe this is not what they expected this position to be, or it is just too different than what they are used to. They have tried, but nothing seems to be clicking.
It happens. At times like these a boss has to do the one thing he probably enjoys the least, let the person go. Be the consummate professional. Sit the employee down and let him know you feel he or she tried and that you hope he or she realizes that you did too. However, you feel at this time that this is not the right position for him, it is not working out for you and you think he should look elsewhere for employment.