This study (a Lancet preprint https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3949410 ) finds that Pfizer vaccine effectiveness wanes from 92% at day 15-30 to 47% at day 121-180, and from day 211 (seven months) and onwards “no effectiveness could be detected”. For AstraZeneca, vaccine effectiveness “was generally lower and waned faster, with no effectiveness detected from day 121 [four months] and onwards”. (The figure they found was actually negative, minus-19%.)
While effectiveness against severe outcomes held up for many groups over nine months, it was found to wane significantly among men, older frail people, and people with comorbidities, contributing to an overall fall from 89% at day 15-30 to 42% from day 181 (six months) and onwards, with a number of subgroups even showing negative efficacy against severe outcomes.
This graph in the paper points out the negative effectiveness against infection at nine months.
Hat tip to Dr. Robert Malone and Dailyskeptic.org