Just to confirm: the first Direct Mode slider (startup) is set to 2/3 minutes and the second one (to stay connected after uploading) is set to Forever?
When the PlayBook disconnects from the Eye-Fi card after about 5 minutes, are photos uploading at the time? Does the PlayBook go into sleep/screen lock mode or something like that? Does the camera power off? What does the Eye-Fi upload icon on the camera display look like - is there an up arrow, or up/down arrows?
The HX9V is Eye-Fi Connected, so I would normally expect the camera to stay on if the Eye-Fi card is still broadcasting its Direct Mode network, even if it's not uploading anything.
Normally it is not a problem for Direct Mode to disconnect after your photos transfer. Just shoot some more and normally an Android device will reconnect within a few second. I should mention that we don't officially support the app on the PlayBook, so it might behave differently than the other devices we've tested, but we can see if it looks like a card issue.
Please feel free to try another test and then post your Eye-Fi card log. Shoot and upload some photos to the tablet, leave the camera on, and wait to see if the tablet disconnects from the "Eye-Fi Card" network. If the tablet and camera remain powered on, but the Direct Mode network is no longer visible on any device, please connect the card to your computer/card reader, click the Eye-Fi Helper icon, choose "Get Eye-Fi Card Log", save the log file and post it here.