Summing L+R mono should not cancel your bass, so check for polarity issues somehwere in signal path. It would be hard to believe that the mixer (even a cheap one) is actually sending the signals out of phase.
One thing to note with canned music though, is a lot of older "classic rock" and similar had poor recordings where L & R bass signals were somewhat out of phase, or just mixed badly, causing serious phase issues, especially when mixed to mono. I have personally found favorable results with "blending" the L & R signals in these cases with my DR260 processor, setting the crossed channels in at about -5db from each other.
That would be (inputs):
channel 1: Left at 0db, Right at -5db
channel 2: Left at -5db, Right at 0 db
That narrows the stereo without completely summing to mono, with less distorted bass on those poor recordings.
With live music, this should not be an issue.