We have stored DNA at -20 for many, many years. It has to be purified by column or precipitation, not a lysate. I have stored lysates for a few months and genotyping PCR still works just fine, but have not tried longer. Pure RNA can also be stored at -20 for years, though -80 is better. I believe the main issue is with the freeze-thaw cycles many -20 freezers go through.
Our DNA and cDNA samples still work fine after stored at -20 for many years, as long as your sample is pure (Dnase free) then should be not an issue. For RNA we stored at -80 as it is more sensitive and more easy to degrade than DNA. If your purpose is for real-time PCR, then it is recommended to convert your RNA to cDNA first as long-term storage might affect your RNA quality and integrity.
Purificated DNA especially in stabiliszing buffers is definitely storable for long-term use, even at 4°C. But less than a week at -20 is absolute nonsense
But for RNA you have to go colder...as mentioned before -80°C