Why does resting potential not become continually more negative?

The resting membrane potential is due to internal/external differences in ion concentrations and very importantly differences in permeability to those ions.

The fact that the sodium/potassium pump does not move an equal number of ions in each direction hardly matters at all for resting membrane potential; the resting membrane potential would be almost the same if that wasn't true. What is important is just the overall concentration of the two ion species, and the permeability of the membrane to different ions (almost all of this permeability is through specialized ion channels, because ions don't otherwise flow easily through a lipid bilayer).

You can calculate the resting potential/equilibrium potential using the Goldman equation - note that nothing in this equation involves the sodium/potassium pump moving different numbers of sodium and potassium ions.

The reason the membrane potential is negative is because the membrane at rest is most permeable to potassium, and because there is more potassium inside the cell than outside. Therefore, there will be a net flow of positive ions out of the cell, until enough ions have left that there is some negative charge inside the cell to counteract that net flow.

As you mentioned, the pump will keep generating an ionic gradient (and the membrane voltage should decrease)

Nonetheless there is still open ion channels at these negative potentials. Then the resting potential will be the voltage at which the net ion Flux (ion channels + leak + pump) is zero.

Since the pump is electrogenic (generates a current) the standard Goldman equation is not applicable and has to be modified.

Here $I_{pump}$ is the current generated by the pump. This equation can also be applied when other electrogenic pumps or transporter are present

You can see the derivation in this paper.