When an electron moves across a resistor, it loses potential energy.
Now imagine a simple circuit (series connection) with the negative terminal having 10v as its potential and positive terminal having 20v as its potential. Now when the electron moves from the negative terminal of the battery to the positive terminal, the energy required to move per 1C from one to the other terminal is 10v.
Fine, but when its moving from the negative terminal of the battery and encounters a resistor in its path, that time its energy is 10v. Now when it passes the resistor (ideally it should lose potential but conventionally due to the positive terminal being at higher potential) it gains potential energy and it is this difference 20-10 which is the voltage.
Now my question is, when it's passing through the resistor after coming out of it, isn't the potential of each electron increasing from 10v to 20v? So shouldn't the number of electrons passing through a cross section in one second increase? I'm somewhat aware of the accumulation of charge thing, the transient period etc., and how it reaches equilibrium. But I would like a concise explanation of this because that doesn't really answer the fact that if there was no resistor there and only a load, then the potential will also increase after a certain point, so therefore the current should too.