As Slava mentioned Heroku doesn't currently have Sticky Sessions so having more than one Dyno will not work. Without Sticky Sessions subsequent requests from the same client will go to different servos and Meteor stores publication state on the server so this doesn't work.
There is a solution to your specific problem of the Dyno going to sleep. First go to your app and then select "+ Get Add-ons" at the bottom, then search for "Heroku Scheduler." This addon will let you run a scheduled task. If that scheduled task is a 'curl' to your Heroku server every ten minutes or so then the Dyno won't go to sleep because it is seeing traffic (even though its form within heroku :)
The scheduled command might look like this:
curl http://www.yourHerokuAppUrl.com/ -s > /dev/null
Select a 1x dyno and a frequency of 'every 10 minutes' and you won't have the latency issues caused by waiting for the dyno to come back from sleeping.