I would guess that autovacuum is analyzing the table and causing the stats to change which is resulting in different estimates that result in different plans. Unless you can get the estimate much more accurate, you won't get far with expecting a stable plan that performs well.
How is data_class_pkey? If you run a query like this, how far off are the estimates?
explain analyze
select d.time as time,d.id as id, a.query_symbol as query_symbol
from
data as d
join data_class as dc ON dc.data_id = d.id
join class as a ON dc.class_id = a.id
where
d.id > 205284974
order by d.id
limit 1000;
If you run 'analyze data( id );' and then run the query again, do you get a better estimate? Have you tried adjusting default_stats_target? Are you running the default value for random_page_cost with SSDs?
I'm seeing Index Only Scan nodes, but a high number of fetches so it seems like you would benefit from vacuum to update pg_class.relallvisible value.
