Here is why this particular clause needs to be amended. First, it clearly states "vacancies that may happen during the recess...". In almost every case, the recess appointments being made are not for vacancies that occur DURING the recess, but have occured long before the recess. But aside from that overlooked technicality, there is a more important aspect to consider.
At the time the Constitution was written and ratified, it took most Senators days, even weeks to get to Congress. They traveled by horseback or carriage. No planes. No highways. So the clause was necessary for national security, as an "emergency session" of congress could take a long time to arrange, leaving America without the necessary leadership.
Today, that just cannot happen. In an emergency, Congress can be called into session within hours if necessary. And if it is not an emergency, then there is no legitimate need for recess appointments.
So, I would suggest that clause be reworded to state something like, "In the event of a national emergency or for purposes of national security, the President may fill up all vacancies that may happen during the recess of the Senate, provided the Senate cannot be convened within three days."
This would stop the abuse - and the perversion - of recess appointments.