This post is only about a minor technological fix to s specific problem, there is nothing about fencing tactics or strategy in it.
After have looked at a team match in which the referee had to remind a fencer that he had consumed his demands for video replay, it struck me that there is a fairly simple fix to this.
Instead of having the fencer demanding a replay, let the coaches of each team have a a small remote that has only one function: to demand a video replay. When there is a referee decision that the coaches disagree with, they simply push that button, and the big fencing box goes into a wait mode, but it shows that a video replay demand has been stated, and by which team. If the referee already has handed out a point, that point is deducted and the box shows the point standing before the contentious call. The bout cannot then be restarted by the referee. Instead, he has to go over to the video table and make his decision, and only after he has had time enough to view the video can he hand out a point based on his final verdict. Depending on whether the final call favors the complaining team or not, the fencing box will show whether that team has any more video replay demands left for that bout. Should the final decision go against that of the demand by the coach, the remote control held by that coach simply ceases to function for the rest of that bout in the team match. Once a new bout starts, his remote is rearmed.
This change requires a bit of new hardware. However, I think that its list of drawbacks stops there. In contrast, is has several positives: The referee does not have to remember whether a given team has asked for a video replay and if so what the outcome was, there is no possibility of a referee granting too many video replays, and no time is wasted correcting a fencer that yes, his supply of video replay demands is down to zero.
For matches where there is a video replay system set up one can be reasonably sure that there will be coaches attending the fencers, so there will not be a problem of who gets to use the remote in individual DE matches.