Just read https://devcenter.heroku.com/articles/logging#writing-to-your-log
I guess you're simply writing to the console. Have you tried to add
$stdout.sync = true
$stderr.sync = true # eventually
to your config.ru or at the head of your app?
Instead of setting sync to true globally, you could also try and do
puts "logging... hello world..."
puts "oh and, this is what happened"
$stdout.flush
flush after each piece of logging, but that's boring.
If you don't log that way please explain in your question and don't count on your readers' divination abilities.