How long can E. coli stocks be stored at -20°C?
I think that cells get damaged at -20°C not because they are stored for a long period of time, but because they undergo cycles of thawing and freezing (the ice crystals that form damage them).

I never keep cells at -20°C. I store them at -80°C in 50% glycerol. The idea behind the glycerol is that it serves as cryoprotecor. It forms hydrogen bonds with the water molecules and thus it disrupts the water-water hydrogen bonds. As a result, it disrupts the crystal formation of ice, and the cells don't freeze. The freezing temperature of glycerol is −37.8 °C (60-70% glycerol in water), which means that at -20°C glycerol does not freeze and thus it cannot protect the cells from damaging from ice crystals formation.