1: The presence of any traces of a bleaching agent such as ferricyanide. You can usually see this however since it'll color the solution yellowish. Minute traces of C41 bleach may be more difficult.
2: Print-out processes such as solar prints tend to bleach back dramatically during fixing.
Perhaps you should tell us a bit more about your processing and the materials used.
Any particular reason for using this relatively slow and low-capacity fixer? You are aware that rapid fixer concentrates are very economical in use, wash out of the paper better and are overall more convenient?
This photo is taken directly on paper and reversed with second light exposure. Reversing is done with bleaching, so this can be the case. Second development was done in VERY diluted developer to preserve shadows going completely black. If I would let it "fully" develop - fixer is not ruining the print.
Considering the process, I might be able to skip fixer all together...
Fixer - simplest one to make myself. Developer, Bleach, Whitening, Stop and Fix are all DIY
With the process you describe you get tiny silver particles, which will happily etch away in this acidic fixer. Use Sodium Sulfite instead of Sodium Metabisulfite and see, whether the problem goes away.
If you want the print to last, I don't think this is going to work.
Maybe the neutral fixer will help a little, but I doubt it. It's worth a try, but I think you're better off changing your reversal process so that it generates a more robust image. It's not too difficult; I played with this on a few occasions and it's relatively easy to make an image that withstands fixing even in a strong fixer (making good positives of desired contrast, however, is always a challenge!)