We always add sample buffer, denature and then store at -20. Also, our samples always contain protease inhibitors. 

To know exactly if it is indeed the storage conditions that are affecting the lower molecular weight form of your protein you should do the experiment again and this time the same lysate should be split into 2 conditions and run on the same gel.

Dear Dr. Abdellatf:

  Cell lysate contained some proteolytic activity and may be degraded during storage process.  So, we usually store WB samples after heat treatment with SDS and 2ME to stop the degradation. In our case, nothing has changed in the target bands during storage period. Stop degradation would be essential. 

Did you detect the 2 bands in Western Blot? If that is the case you know you have degradation and it would be wise to follow previous recommendations of storing your protein after denaturation and reduction which will inactivate any protease present in your sample. Some proteases retain residual activity even when frozen, and during during prolonged storage and during thawing they have plenty of time to chew up your protein.

Some proteins are more susceptible to protease degradation, the above are just general recommendation which should be adjusted case by case.

thanks guys for ur valuable discussion and comments

actually, it is opposite to what u mentioned here, the denatured stocked samples give us the 2 bands, and the other native stocked sample give us 1 band when we mixed it with loading buffer and do the denaturation just before the running the gel.

so the activity of protease is not the issue in case of stock native protein solution, but the second band appear when when stock it with sample buffer.

anyway, we going to repeat all the steps simultaneously and compared them together.

I will keep u updated

Thanks