No, the FBI's decision not to refer Hillary Clinton will not put the matter to rest. It is clear to the American public that Clinton violated federal law in multiple ways. The fact that she is not being referred for charges simply makes it look as if James Comey was improperly influenced. The House has already indicated that it is considering congressional hearings about the issue, so it does not appear to be going away.
No, the issue will not be put to rest simply because the FBI recommends no criminal against Hillary Clinton. The issue will still be talked about and relevant for as long as Hillary Clinton is in politics. People who disagree with Hillary will always mention what she has done in the past to try to shed a light on her mistakes. The media, for one, will never stop mentioning her past headlines. This is because the media is always out looking for the latest gossip and news stories to turn heads, and as long as Hillary Clinton is in the spotlight, no one will let her forget this time in her life.
No, even after the FBI recommendation I do not believe the issue regarding Hilary Clinton will be put to rest. There are a lot of people who do not like/support Hilary and I believe they will continue to speak out on the issue. I also think many citizens will want to better understanding the FBI's recommendation and their reasoning behind it.
The primary issue belying all of this is whether or not the citizens of the USA can trust their political leaders. At this point, it seems rather clear that we cannot trust them. Hillary Clinton is merely one of many that have betrayed the trust of the American people, and there is likely to be more backlash until we forget about it, as a nation, and choose to move on (5 or 6 years from now, maybe).