Actually, Ukraine does have a high mortality rate. Very similar to that of Russia, possibly even slightly higher. I wouldn't trust pdq's source for its exact position in a "mortality league table" but it IS much higher than western Europe and similar to nearby areas of Russia and Belarus. Source for this is:

Ukraine: The Social Sectors during Transition
A World Bank Country Study, 2010


There seem to be various reasons:

- a high incidence of smoking/ smoking-related diseases
- a high incidence of high blood pressure
- a very skewed demographic due to wars, famines and Soviet-era purges
- poor pollution controls in the industrialised east of the country
- low birthrate

Since the end of the soviet era there has been a gradual improvement, but the older generations were born and brought up under those conditions and what we are seeing now as those generations die off early is the consequences of the pollution, deprivation etc they lived their earlier decades under. Mortality rates dropped significantly between 1980 and 2010.

This has been compounded since independence by the aspirations of a large proportion of Ukrainians to adopt a western lifestyle (ie fast-food diet, less physical exercise) but without improving very much on the existing healthcare infrastructure.

Yulia Tymoshenko's government started a programme to improve health care in 2009 but this was largely emasculated when Viktor Yanukovych's government came into power in 2010.