We recently covered a growing thread over at the XDA Developers forum with Windows Phone owners reporting an issue with the on-screen keyboard disappearing from view without accidentally pressing the "back" capacitive button. We were told that Microsoft is currently looking into the problem.
Greg Fonta, a French Windows Phone developer, has investigated the root of the problem. It appears to be related to a Mango feature (as seen in the above video), Background Agents. These agents allow apps to run tasks when currently inactive and not running in the foreground.
According to the report at WMPU, disabling Background Agents appears to rectify the issue. This can be accomplished by navigating to Settings > applications > background tasks and disabling Background Agents on a per application basis.
Does this workaround work for you? If not, which handset do you own that experiences the problem?