The CRS on all three layers are the same. I have tried deleting the PRJ file and reloading. I have also tried Vector> geometry tools> check validity with no errors.
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According to the metadata for your point layer, there seems to be a problem with the extent:
In layer spatial reference system units
I believe this is the cause of your points disappearing.
To rectify this, re-save the layer using the Save As... option and select the relevant CRS (which I assume is
EPSG:27700, the same as the other 2 layers). You should now be able to zoom into the points: