I'm less unsure than my esteemed colleague: proactively protecting questions is a stupid idea, and you should never do it even if the system does allow you to do it.
All "protect" does is prevent answers from folks who've never gained any reputation on the site. It's great for stopping spam and kibitzing on certain types of answered questions (hence the logic in automatically protecting questions with three deleted answers from low-rep users), but can be counter-productive if a question hasn't been conclusively answered yet. Even on answered questions, the existing answers may go out of date, or may attract someone with unique expertise who could contribute something of lasting value but for this restriction. "Protected" status does not expire - that should tell you right away that it's meant for the long-term, not temporary bumps in activity. From the blog post announcing this feature:
We needed this because some of the more popular Super User questions attracted a lot of noise from random drive-by users who didn’t understand how our system works — users who helpfully provided so-called answers like “thanks, this worked for me!” or “I have this problem too, can anyone help?” And lots of them.
Now, there are certainly questions that are very likely to attract crappy answers, and some of these are pretty easy to identify. They should be closed and/or edited to discourage such answers.
A very popular question that starts to attract noise can be handled in a number of ways. Answers can be down-voted, deleted, or improved. Moderators can temporarily lock the question, if it has one or more satisfactory answers already. If it's a real train-wreck, it can be closed and deleted. And, of course, it can be protected - but realistically, this should only be done if it's already well-answered and attracting a large amount of attention from new users. In those rare cases, if the question is still too new for you to protect yourself, just flag and ask a moderator to do so. They are just the sort of exceptions that moderators are around to handle.
In response to some of the comments: don't let some abstract ideal of perfection (a good, popular question with only one answer that conclusively solves the problem for everyone for all time) get in the way here. I'm more surprised to find a common problem asked about without multiple answers of varying quality and helpfulness - this is really only a problem if bad answers become so numerous that they outrank and obscure helpful ones, so focus your efforts on those cases. A question with five answers, where one of them is lazy and low-ranked probably isn't worth your time unless it is distracting.