Can confirm FlyBE is removing FRA-BHX from their booking system, last flight 24th July.
Perhaps a significant proportion of passengers to FRA via LH were using it as a connection?
Yes, I'd say >75% of passengers using LH's FRA-BHX (operated by BD) are for connections (judging from who's starring at the departure monitors when you land at FRA, and gets nervous when there is a delay). It's very popular for e.g. GVA, TXL or VNO, in addition to all the long-haul at FRA. Yes, LH now has FRA-BHX exclusively.
Did FlyBe codeshare to provide connections?
They had a BA codeshare on some flights, which I think was there esp for the Korean Air jumbo sitting in FRA (via OneWorld). But I didn't get the impression this was used much. So you could call this also a points victory by StarAlliance over OneWorld.