The RNA vaccines at least specifically target the part of the Covid virus that makes it special compared to other coronaviruses. If that part mutates in a way that invalidates the protection caused by the vaccine, it almost certainly renders the virus harmless anyway.
Even if the protection does expire, there is no reason to believe it happens at flu-like timescales. Of course if by (is that the right preposition btw?) "constant refreshing" you mean every decade or so, that is possible.
There is also empirical evidence by now:
- https://www.nature.com/articles/d41586-021-01222-5 (protection against variants)
- https://www.nature.com/articles/s41586-021-03738-2 (lasting immunity)