From the equation E(ri)=beta*(rm-rf) + rf , the expected return on any stock, the rick premium is the quantity (rm-rf). So, if the risk premium is small changes in beta become insignificant. Since you are multiplying beta by a really small number close to zero, then beta*(rm-rf) goes to zero, and you are left with the risk free rate.
The opposite is true for large risk premium. The larger the risk premium, the closer you get to beta. This will result in a higher expected return. The risk premium only depends on nondiversifiable risks, which include market and systematic risk.
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