Beyond Mesopotamia, there wasn't a lot of fertile land in which to expand (unless you wanted to invade Egypt), and the people between the rivers were quite aware of the effects of soil salination. So, there were policies to deal with it in most kingdoms -- mandating crop rotation and leaving fields fallow one year out of three IIRC.
However, when the authorities needed more tax revenue (war, new palace, really hot princess to impress, etc.), they'd waive that one-year-in-three rule. Over time, the rule was waived more and more, and eventually there weren't enough fallow periods to preserve the soil. Population crash ensued, so the late kingdoms (1st Milennium BC) had populations less than half that of the middle kingdoms.