The problem here, unfortunately, is on Microsoft's end: Outlook takes too long (up to 20 seconds, compared to well under a second for other apps) to reply to our request for window information via the Accessibility API—but only when Outlook is in the background.

We've had a contact at Microsoft talk to the Outlook team about this problem, and it will hopefully get resolved in a future update. At present, however, there's no fix available. This is Microsoft's explanation as to what causes the problem:

It's a side-effect of the background processing Outlook needs to do to keep networking performance high. Lower priority tasks, like Accessibility API requests while Outlook is in the background, sometimes get dropped or delayed.

As something of a workaround, you can experiment with giving Witch a longer timeout period before it "gives up" on windows that aren't responding. To do that, move the "Application response timeout" slider on the Advanced (Behavior in Witch 3.x) tab of Witch's Settings screen:

The problem is that as you increase these delays, you're increasing the amount of time before the Witch panel appears. At some point, it doesn't make sense to wait for Outlook. (In one test I ran, it took over 20 seconds for Outlook to respond.) In addition, Outlook's response time can vary, so what may work now may not work later.