Hi brash, one of your screenshots shows this:




But that is expected that you will not find a "perp" snap in that spot - perp snap in that case of relocating a construction line will find this perpendicular here from the previous point going towards the curve:





Are you possibly trying to locate areas on a curve where the curve tangents are aligned to the x or y axis directions?

If so then check out this recent post about doing that:
http://moi3d.com/forum/index.php?webtag=MOI&msg=5758.1


The single "Perp snap" will not give you the point you are looking for there - but there are other methods you can use to get it, either select the curve and use the BoundingBox command (set up either a keyboard shortcut for it or hit the tab key and type in BoundingBox and push enter) to generate a bounding frame which will then have intersection points at the spots you want, or set up parallel lines or construction lines and use perp/perp (note - the double perp on both sides, not just single perp snap) as shown here in blue:

http://moi3d.com/forum/index.php?webtag=MOI&msg=3042.14
http://moi3d.com/forum/index.php?webtag=MOI&msg=3042.13

- Michael