How long will cooked shrimp stay fresh in a refrigerator?
According to the Clemson University Extension article "Safe Handling of Seafood" cooked shrimp stays good in the refrigerator for 3-4 days.
More detailed research indicates that cooked shrimp stored in the refrigerator should be eaten within 1-2 days. Considering that thawed shrimp was pre-cooked when purchased - and you do not know the exact conditions that the frozen shrimp was shipped and/or stored - it's wise to discard after 2 days. Thawed cooked shrimp should be used within a few days - the earlier, the better.
The sooner defrosted shrimp are cooked after being exposed to room temperatures, the better. Fresh shrimp should be OK for a few hours, since they will be immersed in boiling water after being peeled. The problem with frozen shrimp is that you do not know what conditions they were exposed to before they were frozen -- or re-frozen.
ANSWER: Unless frozen, shrimp breaks down rather rapidly. If you peel and de-vein, and soak in salted water, you can keep shrimp in a 34.5 degree refrigerator for up to 4 days. After that the shrimp will spoil. Fresh shrimp and fresh seafood should have no odor when purchased fresh and the eyes should be clear and not clouded.