Such stationary marks can signify either a fungal infection
, allergy or a fixed drug reaction
. You should review his intake of medicines. Even simple pain killers can cause such reactions, such as aspirin or infant ibuprofen
. Fungal infections are rather more common in tropical climes, so it may be less likely, unless there is intense itching, or the mark has redness in the border areas and scaling (you can appreciate scaling if you go close to the mark and look for dead skin cells much smaller than but similar to the scales of a fish).
If the local antibiotic
hasn't worked, consider visiting a good dermatologist
, who may prescribe other types of medications, particularly, mild and non-harmful steroids that can resolve the rash as long as he/she considers it to be non-infectious.
Hope this helps.
With best wishes for his speedy recovery,