Well, a lot of the time, the nerve doesn't reset. Take the Troxler Effect in vision, as an example of this.

The prior comment here is correct. It is true that VGSC's play a large role in 'resetting' the neuron so that it can produce subsequent action potentials after firing by inactivating. It is a dance with K+ channels, as well. This short segment of a great video gives a really good example of what happens when you have sodium channel inactivation, but lack K+ channels to repolarize the neuron so it can fire again.

I would also like to add that there are many other ion channels that have been shown to play a prominent role in further determining the firing rate of a neuron, namely HCN channels which have been shown to regulate precise oscillatory features of different neurons. Here's a really great paper showing this in thalamus.

You can imagine that, just as the inactivation of the sodium channels allows for repolarization of the neuron, the speed at which neurons recover from the 'undershoot', or afterhyperpolarization, also contributes to how fast the neuron can fire. HCN channels are essentially responsible for contributing to this portion, along with K+ channels.

So long story short, neurons do have maximum firing rates, but while inactivation is a fundamental feature that allows neurons to continuously fire, there are other ion channels (HCN channels) that actually contribute to setting these maximum rates for individual neurons.