This may not 'walk of shame', but being a loyal customer to the LBS where I bought my bike, once when I had a flat (the only time in that bike's life time, which turned out to be a punctured rim tape), instead of getting it fixed at one of the several bike shops within 3 minutes of walk, I took the bike to the subway (carrying it down/up stairs), walked 20+ minutes from subway station to the LBS to have the tube replaced. My shame here is not the loyal walk, but maybe the fact that I couldn't fix the flat by myself.