After applying the topology simplification mentioned in the answer Remove Slivers/Gaps generated after TopologyPreserveSimplification? It is retaining the topology but is removing the polygon. Below is the image and sample shapefile data for the same (https://github.com/gizmogaurav/spatialPoc/blob/main/poc.zip) Tolerance = .001
As far as I can tell one of your polygons is "invalid" though QGis's validity checker disagrees with me.
As for why polygon 5 is not rebuilt, it seems to be related to the line in red which
Polygonizer reports as a dangle. So again there may not be an exact match across those two polygons. Snapping to a grid might help but I haven't tried it.