It really looks like it has been resolved for me. Now a few days later, and I don't think I've had even one single repeat. And I haven't heard the kids complain about it either :)
What did it for me (I really advise you to try this as well) was:
* [@STEVELEA tip] took out my USB extension cable and put the Flirc directly in the RasbPi (I now have the USB memory stick on the extension or it won't fit)
* [@COBELS tip] did the troubleshooter in the Harmony software and put the value to 1 (it was on 3 or 4 - can't remember)
STEVELEA and COBELS are now officially my heroes. Thanks guys (assuming you're guys that is...)