Some people say anecdotally that the best time for them was when the IRS first opens at 7 AM.
Overall it's unpredictable, and I've read that only about 10% of calls reach a live IRS agent.
If you continue to have a problem reaching an IRS agent, you can see if the IRS Taxpayer Advocate Service will help you or suggest something. If they can't/won't help you, ask them if they can transfer your call to an IRS agent. I've seen a couple users say that at least for them that was a backdoor route to the IRS.
If you want to try that, go to the following IRS website, find the USA map, and click on your state, and it will give you the number of your IRS Taxpayer Advocate.
http://www.irs.gov/uac/Contact-a-Local-Taxpayer-Advocate
Also see this article for more info on how the IRS Taxpayer Advocate Service works::
http://www.irs.gov/taxtopics/tc104.html
