So they had 20 days in which to ask for an 'instruction' phase to be opened. Once that deadline passed they had another 20 days to request hierarchically that the investigation should continue. Had they offered to do the reconstruction I think that would have been carried out.
That's not my understanding at all.
Mine is that the situation was that the prosecutor had weighed up what was in the files and had decided that there wasn't enough evidence to charge anyone.
The McCanns could have argued that there
was enough evidence to charge X on the basis of what was already in the files. Or that there was a clear indication as to where Madeleine was and what had happened to her.
Failing that, they had 20 more days to get the PJ to check out a, b, or c to see if that could lead to fresh evidence to nail X (and hopefully find Madeleine). Technically, that would have kept the investigation going for however more days were needed for the PJ to check out the specific points.
As nothing emerged during that time to be able to consider laying charges, the case was formally archived.
What on earth would have been the point of asking for a reconstruction? The prosecutor had decided to archive it despite the fact that the recon hadn't taken place. It wouldn't have set the investigation clock back to zero.