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Some forms of network access appear to work in the background - apps can finish an upload they've already started, for example, or keep a streaming music connection going - but thus far, we haven't been able to get the level of network access OmniFocus needs to do sync in the background. We file the upload/download requests, but they get paused when another app comes forward.

We're going to take another look at this once OmniFocus for iPad is finished. Until then, sync just suspends itself, then resumes later.