In Platinum, I once tried to catch a shiny Beldum in the desert. I put a Magnezone with Magnet Pull in the first slot, defeated 40 Beldum and saw a grass patch with white sparkles. I checked it and encountered a shiny Beldum. I sent out a Haunter, weakened it enough and started throwing Repeat Balls, but it kept breaking free and eventually knocked itself out with Struggle.That's when you say, "Eff this noise" and pitch out the Master Ball. Beldum is an absolute PITA to catch. The only time I skip the Master Ball is in the Max Lair; you can lob whatever at them and you're guaranteed a catch.
Mine involves trying to chain Beldum on my own copy of Pearl back in the day. I got a few KO'd, kept going but inadvertently walked into the wrong patch of grass and broke the chain. So I hit reset in order to restart my chain.
I didn't hit reset fast enough.
Sliding into view was a Vibrava. It wasn't green. Instead, it looked kinda... brown. It was shiny. I had just reset on a shiny Vibrava and all I could do was watch the screen go blank and the game restart. I felt like someone had punched me in the gut. It. Was Awful.
I tried to chain for the blasted thing multiple times: nothing. I tried to breed: nothing. I tried the Friend Safari in X: nothing. It honestly looked like I would never see the little so-and-so ever again.
Fast forward to an online Max Raid battle earlier this year. It was a Vibrava. The animation started up, I'm standing in front of it with three other PCs, the Vibrava does its little shudder and shake....
I do a double-take. The color didn't look normal but I thought it might have been the lighting form the Den. At least, until I saw the sparkles.
Yep, shiny. I finally found the little blankety-blank. Needless to say, I caught it. I made sure that I caught it. It is mine.
I named it Mirage. Because why not? 
