I've got salty red clay, pure ocean bottom sediment here so I know what you mean by corrosive mud. That bike might have had some bad, leaky welds on the frame from the factory or clogged up tubing drains. I watch mine closely, can't allow rust to get a head start anywhere.
Yours looks repairable at this point though. You could cut some tubing lengthwise and weld halves onto those bottoms, then drill drain holes at the lowest points to get several extra years of service life.