The first study is clearly underpowered to say anything about the risk after more than around 150 days. This can be seen in figures 2 and S1, where the confidence intervals get larger than the effect size at around this point. Combining multiple age groups together also leads to a large risk of getting incorrect results due to Simpson's paradox [1]. But with so little data, the authors probably couldn't stratify for age groups without the confidence intervals exploding.

A much larger study from the US [2] shows no measurable decline in the protection against hospitalization due to COVID over more than 5 months after vaccination.

[1] https://www.covid-datascience.com/post/israeli-data-how-can-...

[2] https://doi.org/10.1016/S0140-6736(21)02183-8

The way I see it, both studies show effectively the same result with similar confidence intervals. The US study however covers a shorter timeframe.

As far as hospitalizations go, I am not arguing with that, vaccines clearly reduce disease burden. The question was: Are vaccines effective at stopping spread? Many countries are experiencing record infection rates with a large majority of the population vaccinated. This suggests to me that vaccines are not effective in that regard.