The key is, empty out your queue of all games except the one you really one (Pro Tip: Make a .txt file on your desktop with what games you want, add them to your queue manually). I keep hearing this is a confirmed as working thing, however I haven't had a game on the top of my list that I haven't received yet, so I can't say this works from personal experience. Worth a try before you quit the service.
This is confirmed...to an extent. The CS rep I spoke with about this issue was like, "shocked" I would attempt this, almost over-acting, because it is "not for sure" you will get a game even if you leave it as your only title in the queue. Truth is, and they will never admit it, is they have to have an algorithm in place that punishes high-frequency renters and older-members in order to give newer, free-trial members priority so they think the service is fast and dependable.
I've yelled at them frequently to fix their availability system, but I think every major online rental service uses the same technology - Blockbuster, NetFlix, GameFly, etc. They all POOL every single "distribution center" inventory to determine availability, but most of the time based on your address, you are "region coded" and if your center is out, but every center has a copy, it will say "AVAILABLE" but you will not get it shipped. This is a really poor system and the way around it is to, sadly, have to clear your queue to "force" a title to ship sometimes. I've had NetFlix and GameFly ship me games from centers not in my region just to get me my title cuz I only had that one in my queue.
NOW, the exception is, like with me, I've called so many times to complain and said I do this to bypass their crappy system and they should fix it, I've seen an AVAILABLE title sit in my queue for days with an open slot, and I've had to call and yell at them and they then say "we're not sure why it says available" and then it changed to "Low" by the time my call ended. So they're sneaky bastards sometimes.
Basically, the best advice is to
1) Only have the games you want in your queue that you want immediately, and save a list of the games you want after if they involve CURRENT RELEASES.
2) If it is upcoming releases, have an open slot BEFORE the game comes out, like at least 3 days, and make that new game the only title. YOU WILL GET IT. Hasn't failed me yet.
3) Call and complain if you haven't gotten a game shipped or hasn't been received. They will clear your spot.
4) If you absolutely must have a title and you sent it in, but you don't think it will get their in time, use the report a title lost feature - it will clear that title out and as long as they get it, you won't get in trouble*
*Sadly, I think they've caught onto this tactic and now it no longer does this. I used this about 3-4 times cuz it was a hot new title coming and I was not convinced they'd get my game and clear the slot in time. Now it won't clear until the game is "received" or "their investigation finishes".
NetFlix is still superior customer service. You call, you get a free extra move sent out. GameFly is getting more anal because I am sure jerks report games lost and just keep them, especially for new games or rare titles.