This doesn't make much sense to me, given that coronaviruses, with spike proteins, have existed for eons, and humans have had lots of time to build up immunity to previous coronaviruses (ones that cause colds, for example). So there was something about the Covid-19 coronavirus spike proteins that was different enough where it didn't look like "familiar" coronaviruses, so I see no reason why it couldn't evolve further to evade whatever antibodies humans are able to build up to the vaccines.
You can make multiple spike proteins that target the same receptor.
This generally happens when a virus from another animal (and thus with a slightly different version of the receptor) adapts to humans.
Basically, a gradient descent from a very different starting point ending up in a different local minima.
The question is, is the spike protein at a local minima (very probably quite close to it), and could it jump to another local minima then? Most likely not.
It's possible it will evolve to make our antibodies slightly less effective, likely as a trade off for infectiousness, but incredibly unlikely the spike protein would evolve to be unrecognizable to our immune systems. Historically, this doesn't happen all that often, except for viruses with chronic infections over years that can do a deeper search over the gradient, but even then it generally takes years to decades.
Given the non-linear dynamics that proteins must live under, I like the usage of local minima as an analogy. It feels apt.
Generally though, within the context of machine learning, one of the benefits of gradient descent, especially when stochastic, is that we can get past those local minima humps. Does this hold less true with respect to the process of sequence mutation that viruses go through?
Another way how to characterize the "context of [deep] machine learning" is that it is the regime of high temperature
(stochasticity) as a result of small batches and/or large learning rates, and/or the regime of high momentum (Adam et al.). The evolutionary dynamics in the genetic space is (intuitively) at much lower temperature (shorter jumps) and with no momentum (because of the evolutionary pressure).
The difference in viruses is that if you get on the hump, you are outcompeted by other viruses that stayed in the minimum, which makes it a lot more difficult.
