Why does the amount of DDT go on increasing at each level of the food chain?

It becomes more concentrated as it accumulates higher up the food chain, predatory species eating herbivorous species end up with deposits in their tissues of dangerously toxic levels. Fish are a prime example, as humans routinely eat predatory fish species (tuna, mackerel, cod, salmon, etc.) which have absorbed the DDT and PCBs (and heavy metals like Mercury) accumulated in the bait species they feed on. The long life span of these species means over time the levels become dangerous. Fish in many places are now considered dangerous to eat regularly (e.g. salmon from Lake Michigan).