My tables are partitioned daily and I still have had issues. The problem is they all still need vacuumed but at least the individual table vacuums are shorter and it makes it easier to drop older data.
I hit this issue all the time and it is never easy or fast to fix once postgres stops accepting writes. If you have a write heavy postgres database, the autovacuum settings are not sufficient. The entire database needs to be vacuumed aggressively.