Since I had the same problem and was able to resolve it, here's a short description of the steps I followed. Maybe this will be helpful to someone.
1) Observe the machine behavior. It's likely that you have nothing to observe - started playback, pops and clicks no matter what you try. But if you are lucky, there could be some hints that might help later. For example, in my case the playback was clean in the beginning, but after I'd start using the MIDI controller, switch to the other windows, etc., the sound artifacts would appear more and more often. This likely suggests a software problem, so I started digging in this direction.
2) Localize the source of the problem. The problem is fairly complex, that's why the first step above is important. The hardware could simply malfunction. There are common-sense methods to check this, so I won't add anything except for one note. If you have an USB self-powered audio-interface, there's a chance it doesn't get enough power from your machine. To check this, you can try using the double-end USB cable (check the image). On the software side one must put attention to the following: audio drivers, DPC latency (google this if you don't know what it is), any other running programs.
3) Eliminate the suspects one at a time, observing the result every time changes are made. The most complex here is the DPC latency. If you are on Windows Vista and later, I suggest that you use the ADK advice from this page, even though there exists an easier to use LatencyMon and such. ADK will give you better results. So if DPC is indeed an issue, you will identify it this way. Drivers: carefully search the Internet for the similar issues on the same hardware/software pair as yours. The newest audio drivers are not necessarily the best ones.
In my case there was a problem with the audio driver. I didn't suspect it though because didn't update it for a long time, and there were no hardware changes at the time pops and clicks started. At the same time, I did VE PRO update, no wonder I suspected it. I checked the DPC latency, and identified ndis.sys spikes caused by NLA service, exactly as in the link above, disabled it, and reduced the maximum DPC latency ever taking place to 256. The problem still persisted. I tried removing any extra VST from the project, and ended up with a single track, low CPU usage, and audio pops. Needless to say, the latency settings in ASIO control panel and in VE PRO connection wouldn't change anything. Finally, I downloaded the 1.21 beta driver from Presonus that I previously avoided because of the 'beta'. And voila, problems solved. Turns out the whole Presonus VSL line has (or had) this issue.