Let me start with the latest page rank drop that several websites and blogs are experiencing, their ranking have dropped from PR 6 to PR 4. Different speculations are been observed but the exact reason for PR drop is yet not specified.

What is page rank and why this is important, what is its significance. Page rank is ranking your webpage worthiness, a new webpage once on the server is indexed by search engine robots, and gradually gains ranking. There are some black hat techniques using which some websites even though are not indexed but have high ranking. If a robot finds broken link that leads to 404 error, it is like visitors return from your webpage without finding any information and these visitors may not come back, in one way you are losing your visitors.

Only broken link cannot be one reason for dropped page rank.

Are you talking about your page ranking/position in the result pages, or are you talking about "page rank" (PR)?

If you lost your position, there are lots of possible factors that could be the reason, if the only one was the broken link, yes your page should gain a better position again in relative short time, if not the broken link was not the only reason for the change.

If you are talking about PR, the loss of PR for a page cannot be caused by a broken link on your page/site.