There's an important detail here -- an advantage of mRNA vaccines is that mRNA does not last all that long in cells [1]. Thus, even if the cells live a long time, they won't produce spike proteins for very long (instructions for the production will be degraded and thus not available).

The vaccine's longer-term effectiveness comes from the immune system's memory B cells response to the short-lived expression of spike proteins.

[1] https://en.m.wikipedia.org/wiki/Messenger_RNA#Degradation