This sounds odd, but try checking 'copper' for your soldermask layer. This should only help if your test points are poured shapes, but it is worth a try.
I've never had issues getting openings iin the solder mask, so there must be a way around this; you just need to find the proper configuration for your CAM setup.
If a test point is a via and you are trying to have Solder Mask opening for the top side, please make sure in Properties - Via Properties - Top Access is checked for this via test point.
From the mail we can understand that the test point assignment is correct ,then the problem will be in PCB fabrication ,check with your fabricator to find out the real issue .
Thanks and Regards
That was it, Yan. Thanks!