Pro tip: mix the pickle juice into the cola BEFORE you ice it, or you'll regret it
Last Friday at my buddy's place in Akron I tried pickle juice in Coke two ways: poured it over ice first, then the other glass with the juice stirred in before any ice touched it. The ice-first glass tasted flat and weird, like watered down brine with a hint of soda, but the stir-first one stayed bright and tangy the whole way down. The difference was about 30 seconds of extra effort and it changed the whole drink. If you're going to try this combo, do the stir first, and let me know if you found a ratio that beats one part juice to three parts cola.
The whole idea that you have to stir the juice in before the ice or the drink is ruined is honestly backwards. Ice melts either way, so once it starts melting you have the same watered down problem no matter what order you did things in. If anything, pouring the juice over ice first lets the cold lock in some of that tang right away instead of letting it sit and go flat while you fiddle with a spoon. Maybe your two glasses just had different amounts of ice, or the second one sat longer while you mixed the first. A real test would be making both at the same time, same ratio, same ice, and having someone else hand them to you so you do not know which is which. Until then this sounds like a fix for a problem that only shows up if you nurse the drink for 20 minutes.