Now that the ranking system has been changed, I've noticed that I don't seem to be changing in rank any more. Even after a long strings of wins or losses, I remain at the same rank. Is this based on a timer or something?
In season 2 your rank is based on your MMR (Match Making Rating) which is a hidden number describing your calculated skill based on who you're beating and who's beating you. You will rank up or down when your MMR moves into the rating required for the next level. There's no real feedback after a game to show you where you stand. You can go into the leaderboards for your division and see where you are in the division so you can see how far you have to go before you rank up. Also, the more games you play, the slower your MMR is going to move, because with more games they've pretty accurately pegged your skill rating.
In v1.13 they've added 5 divisions within each of the Skill Tiers. So if you are in Division I, you are on the low end of your tier and at risk of being demoted. As you move up through Divisions II-V, you get closer to the promotion stage. Once you progress out of Division V you'll be promoted to the next tier.