Staff left because of manager, not job

Attrition rate in this organization is not alarming, less than 1℅ for the first quarter 2013. But when technical engineer left, one with critical skill and well-trained, HR people felt bad. The cost of recruitment is not worth it.
During one of exit meeting, one of the reason quoted was the manager did not deliver the promises, not helping at all when approached. Yes middle managers are overloaded in this company, I am one of them. Organizing Staff Appreciation Dinner, developing offshore technicians KPI,  leading HR team in due dilligence for brownfield takeover are some tasks I am expected to complete in May 2013.  So when the resigning staff said his manager is one of the reason he decided to resign, I am not surprised at all. I have 7 staff under me, all running on auto mode. Except junior staff who need handholding a bit longer.