What it does do is make it public, and the question then is, "Will anyone read it?"
If some guy sets up a blog and starts saying that Rick Warren has 3 wives and practices Shinto in his basement at an altar to his father's father, the first question is, "Did anyone really read that?" And the second question is, "Can that be proven at all?"
That guy with a blog may never delete his blog, but if no one ever reads it, the only one who will judge him for it is Christ -- which is, of course, certainly bad enough. The tree fell in the woods, and nobody else cared. So "permanent" is a bizarre category for what is different about criticism today.
I'd also like to add that the attribute of "constant" criticism is only borne by those who are doing something which somehow keeps drawing attention -- usually to their foibles or errors. For example, I am unaware of Mark Dever having to field "constant" criticism -- unless I should have read [insert your fav watchblogger here] lately or something.
Let me suggest that pastors who are "constantly" in the scopes of critics either have established themselves as opponents of a very active but vulnerable enemy, or they are doing something which deserves criticism. There may be a third choice, but I'll bet if you can find one, it's really the first choice.
For example, there was a time when Phil Johnson took a lot of guff from Fundamentalists. Phil had made some statements -- which he stands by -- criticizing the problems with their movement, and the defenders of Fundamentalism came out of the woodwork. The problem, however, was that Fundamentalism was both very active (in numbers, anyway) but also very vulnerable -- and the advocates for such a thing had to try to push Phil over because, well, if he's right the movement was dead, dying, or worse.
The other example I'd tender is Joel Osteen. Why does Joel take guff from people as diverse as Michael Horton and Steve Camp? It's because Joel is off the apple cart, out of the street, down the storm drain, and rolling down into the swamp outside town.
Criticism is not just hard to bear because it seems to come often. It is hard to bear either when it is the truth or resembles the truth enough to cause us to pause. False criticism is pretty easy to bear unless it costs us money or prison time -- the rest of the time (like when people call me "mean") it's good for a laugh just to see how far someone will take their imaginary world.
And here's the punch-line: how we behave when we are criticized tells us a lot about who we are as people.