Those on here who would get rid of Tim "whether he has MH issues or not", or who would intentionally "manage him out" because he is too much of a hassle to have to deal with, would be breaking the law.
The law is clear that the employer's obligation towards their employee in terms of supporting MH challenges, which could be classed as a disability (it isn't clear from the info given) commences from Day 1 of employment They don't get to pick and choose the nice easy bits and discard what isn't convenient or comfortable, they have a duty of care to all their staff, as human beings. We can all succumb to a physical or MH disability at any stage in life, so let's remember that if it would ever happen to us we would want to be treated with dignity and humanity. So Tim deserves that treatment. Disabilities can come and go, once a person has a diagnosed disability, even if the disability is somehow resolved or mitigated through treatment, they are still protected under the law for that disability,
Those who place the burden on Tim to disclose his mental health issue are misinformed as to what an employee is obliged to do. They do not ever need to disclose a MH issue, and a large number of people elect not to disclose if it saves them being exposed to negative attitudes as on this thread. That's why the Equality Act exists, to put people who struggle with disability on a level playing field with others who don't have that daily battle. Once they have disclosed, then the employer cannot conveniently "forget" that disclosure as if it were an inconvenience.
@cocochanel73 Tim has made 2 more mistakes which have taken me a lot of time to rectify, and could have potentially cost approx £500 in losses.
It isn't clear from your OP whether Tim's mistakes were specified as improvement points in his PIP or were they different errors?
Some points to consider:
Are you sure he has received adequate and thorough training to be equipped to do the job you need him to do? If there is a process he needs to follow, has he been given supporting documentation, eg: describing the end to end process (within reason), or has he been told to do parts of a process without seeing how it all fits together holistically?
Was the training delivered in a way that Tim could assimilate the key information as delivered. People have a variety of different learning styles, as to how they take on board and process information (visual, learning by doing, reading, verbalising).
Some people need extra time to process information, and may need a follow on session to ask questions. Has Tim been offered any follow-on mentoring?
These are a few considerations to cover with Tim when he returns. Have a proper conversation with him, engage, find out what's happening, don't just tick a box and think it's sorted. That's not what being a good manager is. And failing to do these steps could see you on the wrong side of the law as an employer.