I will definately agree with you that "average joe" is far more aware of the name "bmibaby" than they are of "bmi" despite the fact that bmi have a national advertising campaign with their "bmibirdies" (I think thats what they are called) as well as big billboards with destinations & attractive prices.
The problem is clearly that they've gone from British Midland to bmi. BMA was a well-liked & respected brand in the communities that they've been serving, and then they come up with this new "dot-com-age" name. I preferred it when it was "bmi british midland" under the original name change. "bmi" sounded cool enough as a new brand, but also kept the name "british midland".
I am not a bmi-basher. I've used the airline & their no-frills airline a few times, and despite the product slowly getting worse, I enjoy my flights with them - the crew are always charming (especially when they find out I'm crew!), the aircraft cabins are often well-maintained & the overall service is very professional & competitive. However, bmi needs to find its footing in key markets, rather than constantly testing the water here there & everywhere.
To step into armchair CEO mode, I think more cities served by baby from EMA/BHX also ought to be served by mainline from LHR/MAN. Despite AGP for example, being fairly low yield, its a popular route like ALC & PMI served by mainline, and bmi's product would be popular. If I was Lufthansa I'd send in a turnaround team, because bmi have the facilities & crew to be one of the best airlines in Europe, as I believe they once were, they just need vision & a good kick up the a*se, which I think LH (or to a lesser extent) SK could give them!
Just my $?0.02