Hi,
If I remember correctly playlists are only visible when you sync with Sony software or under other menu in playlist or similar.

I had Sony NW-A40 long time ago and remember there was additional step to load external (non Sony app synced) playlists.

Can you check the storage itself and see if the Playlists are really not there? Or perhaps they are, but empty/not being read by the device.

Been using a Sony NW-A55 with Media Monkey for just over three years with minimal problems.
Then, a few days ago, I did a routine synch and all the playlists on my device vanished and refused to re-synch.

I've turned off synching playlists and turned it back on. Mounted and re-mounted my SD card. Power cycled my computer and device. Updated Media Monkey. Redownloaded the device profile. And more.
Nothing seems to work.
Every time I launch my Walkman is says there are no playlists.

But I can create playlists on the device still. The function is still working. Media Monkey just in not transferring the files to the device anymore.