I  live in Miami, florida and lately my cakes keep tilting and melting to one side.

Once I place the fondant and start to layer my cake the cake itself tilts and then once taken outside the fondant starts to melt.

I am also supporting my cake with rods and each tier has its own cardboard plate.

Please help I must be missing a step.

are you using homemade fondant?

Did you chill your cakes allowing them to set up?  I usually level, fill and chill for at least 1/2 hr, longer if I can.  Then crumbcoat and chill some more.  This makes all the difference in the world.  When cakes are too soft the weight of the fondant will bring them down.