Storing the sample in RNAlater reagent would stabilise the RNA, hence can be stored for a longer period. Following are the appropriate resources for your question:
1. Bahn S, Augood SJ, Ryan M, Standaert DG, Starkey M, et al. (2001) Gene expression profiling in the post-mortem human brain--no cause for dismay. J Chem Neuroanat 22: 79-94.
2. Soutourina O, Cheval L, Doucet A (2005) Global analysis of gene expression in mammalian kidney. Pflugers Arch 450: 13-25.
3. Cookson W, Liang L, Abecasis G, Moffatt M, Lathrop M (2009) Mapping complex disease traits with global gene expression. Nat Rev Genet 10: 184-194.
5. Goh K-I, Cusick ME, Valle D, Childs B, Vidal M, et al. (2007) The human disease network. Proceedings of the National Academy of Sciences 104: 8685-8690.
That would depend on the reagents or chemicals in which your tissues are stored. For instance with RNAlater your can store tissues for months to years at -20 or -80 oC without compromising the RNA integrity. With the same chemical preservative you can store at 4oC for about one month or at room temperature for about one week.
RNAlater is highly recommended for soft tissues such as liver, kidney, small intestine e.t.c But if you work with material such as bone or cartilage, in which therefore the RNAlater cannot penetrate the tissue, it would be best to keep them at -80.
I have had tissues and RNA stored at -80 for up to 2 years and the RNA is still absolutely fine.
RNA is completely useless and broken down in 15 minutes of fresh extracted tissue. Different RNAs all have different rates of degradation and there is no way to be sure your RNAs of interest or their controls will be similar. Sure, perhaps you could extract tissue quickly enough and freeze it, but you still need to thaw it at some point, and your RNA will be directly affected.
Don't leave your samples to whim. Stabilization reagents are cheap when considering the benefit they provide.