QUESTION Current is constant throughout the circuit with a resistor hence we cannot say that the electron loses kinetic energy after passing through the load.
SOLUTION Current throughout the circuit with a resistor is constant , no doubt about that. But to be fundamental, current in a circuit is set up by the electric field, not by electrons. For instance if there are 100 bulbs connected in series in an electric circuit, on switching on the cell, all the bulbs are lighted at the same time, clearly proving that electric field and not electrons set up the current. Again electrons have a very low drift velocity of a few $mm/s$ as they suffer a large number of collisions among themselves. And yes the electrons do lose kinetic energy and that is dissipated in the form of heat in the resistor. The external energy supply i.e. the cell in this case supplies the necessary energy to keep the current constant. That is the sole loss in energy in our domestic electrical circuits, i.e. to say Loss in K.E. of electrons = Heat in resistor. $$ E_{cell} = Work_{electrons} + Energy _{dissipated}$$
QUESTION So what changed when an electron passes through a load that causes the load/resistor to heat up while the potential drops?
SOLUTION As the electron has to overcome some electrical resistance, it does some work which is dissipated in the form of heat. And potential difference being the driving force of the circuit, current flow is resisted in a resistor and as current prefers a resistance free medium for propagation, the driving force of the current lessens and across the resistor, there occurs what we call "a potential drop". It can also be verified by using Ohm's Law.
I explained this in layman's language. Hope it helps.
