On services such as Heroku, you have the option of using what is called SSL Server Name Indication (SNI).
Unfortunately, currently, StillAlive does not support SNI SSL. Our service will detect this and throw an error saying that the hostname and SSL certificate do not match.
The solution is to use the "site-name.herokuapp.com" domain name for your site. This will then verify correctly against the SSL cert that Heroku is passing back.
We have upgrades in the works to allow for SSL SNI certificates, but in the mean time, the above is the best work around.