Question

Why an electrochemical cell stops working after some time? and what would happen if no salt bridge were used in the electro chemical cell?

Answer 1

When one compound of in the anode of electro chemical cell is oxidized, those electrons serve to reduce the compound at cathode side. When the material at anode no longer has electrons to loose, the reaction stops and cell stops working. 
If no salt bridge will be used, electrons were not able to shift sides and the reaction wont start and cell wont work. 

Answer 2

Explanation:

When one compound of in the anode of electro chemical cell isoxidized, those electrons serve to reduce the compound at cathode side. ... If no salt bridge will be used, electrons were not able to shift sides and the reaction wont start and cell wont work