Izzy's actually not one to give up easily. She'll take a lot of crap before she decides to quit. But she does have her limits. Typically those include the times where she's just too dejected to do much of anything else. You've seen that a couple of times a while earlier when Izzy found out she didn't get into the handler program and the following day.
Izzy's kinda too tired and sad to fight what she's going through right now. Maybe best to give up before things get worse.