It turns out, I am not the only one experiencing this. Maemo Bug 2850 deals with the same. I found comment #8 interesting, as it provided the fix.
It turns out that you can type the following within xterm, and the on-screen keyboard will re-appear:
gconftool -t bool -s /system/osso/af/slide-open false
I added this command to the list within osso-statusbar-cpu. Now, whenever my on-screen keyboard disappears after I use my bluetooth one, I am a few clicks away from restoring it. Sure beats having to reboot or to use the command line!