Tips to prevent burnout?

Not a lot of context here, hard to provide any relevant advice.

Why are your Scrum events tense?   

Why does this team member struggle under these circumstances?

Is this behavior noticeable to the rest of the team?   If so, what do they think/suggest?

My thoughts are whether this team member is able to contribute positively towards the sprint/project goal (other than finding the events hard to participate) or working with far less focus and commitment

- if this tension is due to personal issues, it may help more if the team member gets a break to sort his issues out. This may need arranging another developer with similar skills if he holds some special skills or facilitating other team members to work with the product owner on reworking the sprint backlog because the capacity is going to be affected

- if this tension is due to interpersonal conflicts within the team, the reasons need to found out before thinking whom and how needs to be coached

There certainly isn't a "golden tip". This is about a human, and it is going to require great care and attention, to understand what the actual problem might be, and the best way to proceed.

I think one of the most powerful things you can do over the long term is help foster a safe environment within the team (particularly during retrospectives), so that they're able to be honest, whilst being respectful.

If you have a safe and caring culture within the team, it could help team members deal with these kinds of issues proactively and more effectively.

But whatever you do, remember that we're talking about the mental health of a person, and coaching might not be the appropriate way of helping.