Let's start with the big one: Robin's age.
First, Robin was created as a way of increasing youthful readership. Having a Boy Wonder attached to Batman gave kids a character they could identify with and live vicariously through. But has that age passed? The average comic reader is significantly older than they used to be, so is having an eight (to ten) year old sidekick really needed anymore? Also, given extensive investigation on my part as to the popularity of High School Musical (Step #1: Grab teen by collar. Step #2: Shout "WHAT IS WRONG WITH YOU?"), it turns out that kids these days are not as interested in characters of their own age so much as characters that are just a bit older. Call it the Cool Older Sibling complex or whatever, but the kids who liked HSM were not in high school.
Second, nowadays, having an adult character pal around with a child in tights is Just Not Done. There were whiffs of this back in the day when Alfred got replaced by Aunt Harriet for awhile. Worries about pedophilia aside, there's also the whole "how could a responsible adult put a child in danger" angle. Of course, we have characters such as Pokemon's Ash and friends whom nobody seems to mind the fact they are essentially hobos wandering around the countryside picking fights with other hobos using wild animals.
Third, in the setting, it took years and years of training for Batman to get to a skill level that was required to fight crime. Dick may have had a leg up on Bruce from the starting point of general athletics being a gymnast and all, but that doesn't mean the kid knows how to fight or ninja climb a wall. Those skills take time. Looking at Dick's timeline, we have his parents dying, Bruce identifying with the kid and adopting him, Dick finding out who Batman is, and then, what? Five years of training in order to become capable of accompanying Batman on a mission? So if we took Dick at his youngest (8) AND assumed that Bruce threw money at the legal system in order to adopt him super quickly AND that he left the door to the Batcave open during Dick's first week at Wayne Manor, that means at best Robin will be starting his sidekick career around 13. While this is fine for our Dick Grayson as he'll be leaving the role of Robin after filling it for 1/2 a SU (so 5-7 years), making him 18-20, just old enough for the "college" of the Titans, it makes picking his replacement a tricky proposition.
The second bit of baggage is why the heck would Batman want a sidekick in the first place? With Dick, you can get away with it somewhat. Batman is still youngish and prone to being impulsive. He was there when Dick's parents died and that no doubt brought back memories of his own. There's a bond of shared experience there and quite a bit of emotional transaction. Dick gets father figure and the chance to strike back at those who hurt him, while Bruce gets to live a bit of the childhood he denied himself through Robin's eyes, plus he gets to be the Action Dad he so wanted his own father to be in the dark alley.
So how does Batman replace that? Emotional bonds aside, if he's become accustomed to having a sidekick, we'll have to assume that he figured out that Dick would grow up and leave the nest at some point, and thus the Master Planner aspect of Bats would kick in and he'd go about arranging for a replacement. Given a five year lead time on training alone, that means that he'd have to have started looking for a replacement Robin from pretty much the moment Dick put on the cape. Awwwkkkwwwaarrddd!
There is an easy way around all this, of course, that that's Option D (for Damian). Damian Wayne, as the son of Bruce and a member of a supersect of terrorist assassins from birth would have the training and connection to pretty much hit the ground running. Which means we can't use him right now and instead must save him for 5-7 years down the road when the current Robin needs to move on.
So who are our candidates and what does each bring to the table? Like Batman villains, who each are some sort of dark reflection of some facet of Batman, Robins need to be little reflections as well. There has to be some common aspect between Batman and his Robin du jour. Dick matched Bruce by way of dead parents and physicality, for example. Each candidate would be adolescents at the start of their career as Robin.
- Jason Todd (The Crusader) - Of the candidates, Jason Todd is perhaps the most driven. Growing up as pretty much an orphan in the slums around Crime Alley, Jason had to do everything himself. His original motivation wasn't a sense of justice or anything, but survival. He did what he needed to do to survive. Nobody else would help him. Over time, this changed into rage. Jason knows first hand how sick a system Gotham is and has a good idea what must be done to correct it. He would come to Batman's notice by waging a one boy war on some of the gangs of Crime Alley, cementing his candidacy when he then tried to steal the Batmobile's tires ("I can live for a year by selling these. You'll have them replaced in a week. Who needs them more, Batman?")
- Tim Drake (The Detective) - The most intellectual of the candidates. He's able to make connections between desperate facts, follow the sometimes twisted logic of Gotham's underworld, and intuit the motivations of people he just met. As a 'fan' of the exploits of Batman and Robin, he spent a lot of his idle time following their career, even to the point of figuring our their secret identities. When his own parents pass away mysteriously, he gathers the information he has about their deaths, and then tracks down Bruce Wayne and demands he does something about it as Batman. ("Being able to prove it and being able to do something about it are two different things, Mr. Wayne. Now, will you help me do something?")
- Stephanie Brown (The Knight) - As the daughter of third-rate criminal The Cluemaster, Stephanie saw first hand the impact criminal endeavors have, not just on the victims, but on the perpetrators themselves. Her father was always talking about 'just one more score' then he could quit, but that day never came. She took it upon herself to spoil his plans, trying to force him to quit the criminal life cold turkey while saving others from the misery her father's actions could cause. More so than Jason or Tim, Stephanie does what she does for the sake of others, not just out of some drive for justice or intellectual pursuit. She honestly feels like this is the best way for her to help others, to defend those who cannot defend themselves (sometimes from themselves). ("About time you showed up, Batman. You take the one on the left.")
So who is it gonna be?