Something is missing from the end of the sentence: ... as a result of political WHAT? "Political" is an adjective and needs to modify a noun. Political arguments? Political infighting?
At any rate, both words -- over or until -- could be correct depending on the meaning you intend.
The country has suffered from little investment over the past year ... means that during the entire year that has just passed, there has been very little investment.
The country has suffered from little investment until the past year... means that until one year ago, there was very little investment, and then, as of one year ago, things changed, possibly implying that suddenly there was more investment.