It seems different from what I thougt first. After repositioning search specs (like Clear, Fav, Fetch, etc. in the docked Binsearch tab) the new layout is not always saved. After closing and restarting AltBinz I most of the times get an older layout of those tabs. However sometimes I get back my most recent layout. I can not find what triggers it.
It has nothing to do with undocking and re-docking, that was just a coincidence when it happened to me the first time.
On the other hand: undocking and closing again seems a work-around. I now change the layout of a docked tab, undock that tab (a random tab seems to work also, I believe), re-position an random item of the undocked tab and then close it. After a restart of AltBinz (and closing the unintentionally undocked tabs; I got 4 of them now) the docked tabs always have my own, latest layout.
Undocked tabs always automatically have their latest layout, it seems.
I hope this is clear enough?