I've given a lot of series a second and even a third chance. Have to admit that i've dropped almost every shonen i've started reading at least once.
1- Naruto: I was put off at first by how the main character was a twelve years old kid. He was dumb, not liked by anyone and kinda weak. During my teenage years i preferred the likes of Bleach with stoic, badass MCs, plus I felt too old and thought i wouldn't be able to relate.Then Shippuden came out and i decided to give it a second chance. I liked it till i got to the time skip, read like 50 chapters and then dropped it. Two years ago i decided to give it a third shot, caught up and read it weekly till its end.
2- OP: I dropped One Piece twice in the same spot, the Baratie arc. I hated Luffy, thought the story wasn't original, the characters lacked personality and weren't remotely memorable. Once i ran out of series i decided to give it a third shot given all the praise it was getting. From Arlong Park on it wasn't that hard to follow but i was still having a rough time because i couldn't see why everybody thought it was that great. Once i got to Water 7 everything changed and i was hooked but it was during SA that i started thinking that maybe One Piece was becoming my favorite series of all time.
3- FMA: I started with the anime (the 2004? version) and boyy did i think it was boring. Then Brotherhood was announced and i thought i should give it a second chance. I got immediately hooked with the manga and followed it through its end.
4- Mobile Gundam 00: Dropped it on the first episode. I fell asleep while watching it tbh. Then my friend forced me to watch it and by the end i was regretting not watching it sooner.
5- Evangelion: Dropped it at first because i thought it was uninteresting, gave it a second chance and i still think it's uninteresting.
The list is endless but these are some of the most famous examples. Kudos to Tokyo Ghoul, Seven Deadly Sins, Shingeki no Kyojin and Magi for grabbing me on the first try.