Having the exact same issue on type 3 UI window (three rows, no boff potraits) since yesterday's patch. Icons keep disappearing when I try to switch the rows. Wasn't able to figure out the reason this is happening.
But disappearing icons are one thing - sometimes I can't put an ability back into specific position. I nearly threw my computer out the window yesterday when I was trying to prepare for the shuttle event.
As for the changing location solution - didn't work for me, although I noticed that removed abilities do in fact appear once again on the tray. The problem is, they're messed up, and still disappear when I switch the tabs.
So now not only the UI tray tends to get messed up when switching ships, but also icons disappear on my very own eyes when I just try to change something. Great job Cryptic...