Working with Sqlite in production is very problematic because each time you deploy new version you entiredb is stay on the old release folder, what you can do is when you deploy add this command:
task :copy_sqlite, roles: :app do
run "cp #{current_path}/db/production.sqlite3 #{release_path}/db/"
end
just add this the before rake db:migrate
and it will solve your problem.
My strong suggestion move to PostgreSQL/MySQL.