they will in fact NOT go away. They will in fact follow you quite closely and whine all the louder.
Long ago and far away, when I foolishly believed that parenting books could actually help me, I recall ingesting the helpful advice that ignoring unwanted behavior would make it simply disappear. I understand the principle here: acting out is often a ploy for attention; hence, any attention, even negative attention, achieves the child's desired goal and puts the control back in his court. But in parenting, principle and practice often seem to be two very different things.
I was relieved to hear off-blog from Rebekah that excessive whining among the preschool set is not necessarily a phenomenon limited to our household. Lately, though, it's been ridiculously excessive (We've had a few things disrupting the routine around here lately, which hasn't helped, but enough is enough!)
So if anyone has whining-management techniques that have proved effective, by all means, SHARE! We've tried everything from the sugary-sweet "Oh, honey, Mommy's ears can't hear you when you use that whiney voice" (HA! Verbatim from another of those parenting books that we gave up LONG ago) to "GO TO TIME OUT RIGHT NOW AND DON'T COME OUT UNTIL YOU'RE DONE WHINING UNLESS YOU WANT A SMACK ON YOUR BOTTOM!" and quite a bit in between...and still the whining goes on. Makes the two-year-old's tantrums seem downright refreshing :P