current of forward-biased pn junction
What you need to understand, is that although Jp and Jn do decay exponentially with distance, at any given forward bias voltage, "electrons will be supplied... to the n region at a rate that will keep the current constant, at the value it has at X = Xn".

Another way to see this, is by analyzing the equation for Jn (or Jp) and noticing that for a particular diode at a given voltage (V), all other variables have a fixed value.
Since Jn (or Jp) ends up with a fixed value, the total current [I] (at a given voltage [V]), is constant!