If you drafted guys like Billy Butler or Cameron Maybin in the last couple of rounds of a normal sized league, they don't necessarily deserve a full month of patience. Your level of patience should depend on the size of your investment and the last couple of picks are not significant investments at all. If I took the philosophy that young players that I drafted late deserved a month to prove themselves, I would have missed out on a number of hugely profitable FA pickups in years past. Nate McLouth from last year comes to mind.
I wouldn't be hanging on to a guy like Maybin in a 12 team mixed league right now. I'd turn to a guy like Nyjer Morgan, for example, and wouldn't hesitate. Odds are he won't be picked up anyway. In fact I've been kicking myself for not simply dropping Maybin for Bonifacio before opening day, given Bonifacio was named leadoff hitter before the season started. Player values are in such a constant state of flux that you just can't get the most out of your roster if you fall in love with the potential of your own players at the expense of recognizing the potential in the players that are currently available. Players are constantly moving in and out of the top 150 or so and the skill to fantasy baseball is knowing when this happens and acting accordingly.
So yeah, I'm not going to wait through 100 ABs for my 21st rounder who hasn't proved anything yet at the major league level to turn it around. There are just too many productive players that emerge during that time.
On the other hand, if I pick a guy in the 10th or 11th round and they had a reasonably good year the year before, sure, then I'll give them some time.