To the best of my knowledge the first COVID vaccine dose immune response is not short-term, except in the sense that it is weaker and therefore will fade below an effective level in a smaller amount of time. But it fades at the same rate as the second dose. The second dose just "raises" the response level higher than the first dose got it.
Couldn't find my original source, but here's another:
> The second shot has powerful beneficial effects that far exceed those of the first shot,β Pulendran said. βIt stimulated [...], a terrific T-cell response that was absent after the first shot alone, and a strikingly enhanced innate immune response.
