Firstly the culture that would have someone take their own life rather than be removed from the things they love doing or to let people down being a motivator to end it all needs to be examined and challenged.
I think we should be wary of rushing to self-criticism here, especially if the culture being imputed is that of the RAF rather than society at large. For every case that erupts into wide-scale awareness there are many more being sensitively, appropriately and discreetly managed. The days of automatic grounding and/or withdrawal of security clearance are long gone. I know of more than one who has carried on flying with a full clearance after declaring MH issues, and others who have returned after a recovery period - but there are no easy universal answers in either field and a blanket policy of turning a blind eye would be just as inappropriate as its opposite. It is good to see that the OP feels able to talk - that means we are doing something right and I hope it helps.
As regards suicide to avoid letting people down, I think this is a wider societal issue and one which afflicts primarily high-achieving men, who it seems to me are more prone to defining themselves by their achievements and progression. And it is an internal perception - from everyone else's perspective, suicide and retirement have identical effects in career terms. People lower down the achievement scale seem to me far less susceptible, being more prepared to subordinate their careers to other priorities. If there is anything organisations can do to help, it is providing alternative career pathways for those who might privately be looking for a way off the ladder. There is some good work going on at lower levels on this, but the "up or out" nature of very senior military careers is undeniably brutal. Very sad to see and I hope the air marshal gets the support and care that he needs.