The first dyno is free, but it doesn't stay booted. After a period of inactivity, Heroku shuts it down if you don't have any paid dynos. When a new request comes in, it take a few seconds for the dyno to boot back up. For users that have little traffic, the dynos get shut down and your requests are very slow when they happen.
Heroku has good reason for this. The number of test apps that people create to try the system and then never shut down is probably quite high. They don't want to be running 10,000x512MB worth of apps that aren't serving any traffic. However, that also means that if you have a low-traffic (but real app) running on their system, the dyno is likely to get shut down during the times where you have no traffic.
A 1/2 size dyno would allow people to have a cheaper dyno that wouldn't be shut down.
At one point in time, you could add the free version of NewRelic along with a scheduler task to keep your free dyno active: https://coderwall.com/p/u0x3nw I haven't tested that... so things might be different now.