Hi Anwar, if you are using the BL21(DE3) T7 expression system, T7 RNA pol is faster than the E. coli RNP, which leaves a naked mRNA stretch between RNP and the first translating ribosome, which in turns makes it more prone to degradation by RNAses. You might try to change your expression system to use the E. coli RNP.
I am not sure I understand. Any transcript synthesized by T7 RNA pol is expected to be less stable than the same transcript synthesized by E. coli RNA pol. The first will be naked for a certain time because T7 RNA pol is faster than the translating ribosome whereas the second will be covered by ribosomes which will follow E. coli RNA pol at the same speed. This affects all mRNAs synthesized by T7 RNA pol but in general this effect is counterbalanced by the much larger number of mRNAs produced by the T7 RNA pol compared to the E. coli RNA pol, which results in a net increase of the produced protein. Now, it might be that your mRNA is particularly sensitive to degradation when it is naked, hence your problem (You don't need to imagine that your plasmid increases RNase activity). I attach a paper explaining what happens in detail. Other more recent papers from the same lab give more information.