Yes, while rare, low platelet counts (thrombocytopenia) may be a potential side effect of Low-Dose Naltrexone (LDN), according to case reports. Specifically, studies of MS patients on LDN, have suggested a possible link between LDN and immune-mediated thrombocytopenia, where the immune system mistakenly destroys platelets.
It seemed to resolve easily when off LDN so you could check by going off the med.

I sympathize because it takes so long to titer up to the correct dose on LDN that going off it can be a real pain.