With any protein, vigorous vortexing is to be avoided because it results in denaturation of the protein and loss of activity. Gentle vortexing is usually acceptable to help achieve a homogeneous solution. The vortexing is gentle enough if no bubbles are created. For a small protein like RNase, this should be fine.

Colder temperatures like -20oC are usually better for long-term storage of powders, although some proteins are stable enough to store at 4oC.

Once you have dissolved the protein, make a set of small aliquots (e.g. 50 ul)  in microfuge tubes, flash freeze them in liquid nitrogen or on dry-ice, and store them at -80oC, if you have access to such a freezer, or a non-frost-free -20oC freezer if you don't.

Thaw an aliquot for use by gently warming it in your hands just until it is thawed, vortex it gently to make sure it is homogeneous, then place it on ice during the working day. If the activity is stable to repeated cycles of freezing and thawing, then you can refreeze the aliquot as you did originally. If not, store it on ice as long as it retains activity, then throw it away.

Thanks a lot for your answer!

It is universal that any enzyme or protein is viable for long term at low temperature like -20 or -80 degrees and should not vortex harshly due to which enzyme may denature and lost its activity. Also it is recommended that once you make the working stock of any protein, divide them into small aliquots and use one aliquot at a time as freeze thaw may reduce the activity of the protein...!!

Thank you, Yogesh!

I agree completely with what Adam B Shapiro  advice ,i recommend you fellow it & you will not loose your enzyme. 

Thank you, Hathama!