When you record a style to Track A of a user song, it doesn't record any portion of the style itself, only the information needed to play back the recorded accompaniment-- namely, the Style Number, the overall Style Volume, the on/off status of each Style Channel, the selected Style Section, your Style Chord changes, and your Style Section changes.
If you're trying to record just the Rhythm portion of the style, it probably isn't going to record enough to play back the style the way you think it should unless you're doing something every so often that the keyboard can actually record to Track A, such as changing to a different Style Chord or selecting a different Style Section. Otherwise, my guess is that only the initial settings will get recorded-- the Style Number, Style Volume, on/off Style Channel settings, and the selected Style Section-- but after that nothing will get recorded to indicate any passage of time. Hence, when you save the recording you basically get a beginning followed immediately by an ending, if you see what I mean, since there were no other style-related events for the keyboard to record.
I would try recording the Rhythm and doing some sort of chord change every so often, even if you've got all of the Style Channels except for the Rhythm turned off such that the chord changes don't have any noticeable effect on the style as it's being recorded. That way the keyboard will be able to record the chord change events at the appropriate times. Actually, you should really only need to do a single chord change, at the point where you want the style recording to end. That way when you save the recording, Track A will end with the chord change, which will occur at a specified MIDI time offset, thereby allowing Track A to play back for the desired length of time until it reaches the chord change event at that specified time offset.
