Small dna and rna diffuse quicker than large molecules and the rate of diffusion depends on the shape of the dna/rna, the concentration of the agarose gel and the temperature of the gel and buffer which is determined by the room temperature and the current that the gel is being run at,
If you are losing bands on viewing a gel then the bands may be fading due to UV photoquenching where the uv light destroys the etbr/dna fluorescence. This happens when you leave the gel on a transilluminator for too long
As mentioned above, both DNA and RNA will diffuse in an agarose gel. Usually this is not apparent as the electrophoresis moves bands far faster than they would randomly diffuse, but bands will become more diffuse after the power has been turned off. However, for DNA fragments above 500 bp or so, diffusion will not effect the banding too much, as we sometimes have left our gels to stain over-night (this allows you to stain with lower concentrations of dye and to reduce the background staining levels)!
The rate of diffusion of DNA and RNA in agarose gels depend on the molecular weight, conformation, and the percentage of agarose in the gels...Smaller the molecule, the faster it will diffuse, whereas, the lesser the agarose percentage, the faster DNA and RNA will diffuse. These conditions are applicable if the power has been switched off. Hope this helps.