I have a number of frustrating memories from my years playing Pokemon, but I'm not sure what the worst one is. In Red, I recall saving in some part of the Seafoam Islands without the Strength user I needed to alter the current. I didn't have any escape ropes, and I didn't recall how to get out, so I wandered aimlessly hoping to use up all of my PP on my overpowered Blastoise (the only Pokemon I used at the time) so I could Struggle myself to death. Somehow, I eventually found the exit (I'm sure it wasn't as hard as it seemed, but at the time, it seemed incredibly difficult, and having saved inside the area the day before, I didn't remember the layout of the place at all). Since that time, I've made sure to always carry multiple escape ropes (one to escape, and one as a back-up in case I forget to replenish my stock after escaping).
As for hax-style irritation, I have a lot of painful memories of trying to beat the Stadium games with rentals. Every time I'd come close, I would proceed to miss repeatedly (the joys of having to use rentals with poor-accuracy moves) or hit myself in my confusion, be attracted, be paralyzed, etc., turn after turn until all of my Pokemon got KO'd. Gym leaders were especially bad, as there were no continues; face bad luck, and I'd have to re-challenge the previous three trainers just to get another shot at the badge. The experience got much better once I started using my own Pokemon (trying to train stadium teams with very limited resources after the internal batteries on my main games died was more fun than I expected), but I still have a lot of bad memories.
I found the Pokeradar in gen 4 very frustrating. I always had bad luck with the thing, even when I followed guides to the letter. Needless to say, I haven't taken up that charge again in gen 6.
And then, the obligatory shiny story: shiny Skorupi in one of those double battles with a supporting cast member in White2. I had no way of taking my partner's Pokemon (Musharna) out with the Espeon I had been training, and of course, which Pokemon does my partner decide to take out first? That poor Skorupi never had a chance. I had a Master Ball ready to go and everything, but of course, there's apparently no way to aim at one Pokemon in a double battle without a snag machine, so I was out of luck. Moral of the story: Always have an overpowered Pokemon at the front of your party in any area where you have to double battle with a partner, and take out your partner as soon as the battle starts. Oh, and hope the wild Pokemon don't knock each other out. Sadly, I've never found another shiny Skorupi.