I definitely would NOT write an open letter to the board. It will just sound like a list of whinges and make you look weak.
Does the board set and agree objectives/targets with you? If they do, and they are focusing on minor errors, then I would ask for a performance review where you can defend your performance vs your targets and set the minor errors in context. If targets are NOT being set, then this is the Board's fault that they haven't communicated what is an important objective and what is not - if they are focused on things that are minor to you but perhaps more important to them.
If they really are harping on about minor errors and not appreciating the big wins, then they are being unrealistic and goh can tell them so. You can point out that a team that risks nothing, achieves nothing.
You give the impression it may be just a few board members who are causing you problems. In which case, I would ask a sympathetic member of the board to have a private mentoring conversation with you for two hours once a month, and use that conversation to do some stakeholder mapping. Is it really important to satisfy the minor niggles of outlying board members? Perhaps not.
I definitely agree with the previous post which says you should take charge of promoting your good work.
Send a regular email bulletin to the whole board, updating them on excellent work done, calling out individuals' achievement and cc senior members of your team if appropriate. When you meet with the board, make sure you ask for 10 minutes to give highlights since the last meeting, and then you can also add in a slide that talks about how important it is to value and recognise everyone in the organisation and talk about morale. Give them some ideas how morale could be raised, and say if the tone from the top was more focused on clearly communicating strategy, focused o major objectives it would be a more positive and engaging place to work. Ask the board to consider doing an all-staff engagement survey, to see how people feel about the workplace and their role.