You are actually measuring the purity when you refer to the 260/280 ratio. I would also pay attention to the 260/230 ratio. 260/280 ~ 1.8-1.9 is acceptable and 260/230 > 2.0. Also, look at your absorbance peak. The nanodrop manual gives some good examples of the different contaminants along with the associated peaks and ratios.
Lastly, you can have acceptable RNA purity (260/280 and 260/230 ratios) and good yield but the RNA could be degraded. However, you would not know this unless you determine your RNA quality with a RNA denaturing gel - 28S band should be about 2x more intense than the 18s band with no smearing of your RNA. Or you can use a bioanalyzer which is more sensitive for purity and quality. In reference to your issue, maybe your RNA samples are degraded. Reference genes typically have higher expression than your target genes expression, therefore, you may detect the former and not the latter if the sample is degraded. If you are measuring gene expression with RT-qPCR, you should observe a shift in your Cq values in the degraded samples as compared to what you usually observe.