There have been a few times in the past couple years that I've had to call vendor support for one issue or another. The way it typically works, I mess around with one thing or another for two or three days, and when I'm finally at an impasse, I break down and open a ticket with support. Then a little while after opening the ticket, I suddenly get an idea that solves the problem, and I either have to tell the support tech when he calls or try to cancel the ticket before he bothers.
It never really dawned on me before why I'm so consistent with solving issues like that, and I was talking to another DBA the other day who gave me the answer -- you know, just a little pillow talk between us DBAs. The idea is that the mere task of collecting all the data and explaining the problem puts all of that info at my fingertips at one time, and I'm able to see what I've been missing.
So to simulate that, I suggest you write e-mails to someone explaining an issue you're having. Include as much info as you can, and outline the exact steps you've taken to troubleshoot. Go into as much detail as you can and give specifics about when the problem occurs and what seems to trigger it. Even though you may not be ready to send your issue to support, writing the e-mail may really help you figure it out because it forces you to pull all the info together.