Thiols will become increasingly deprotonized at pH > 8. The resulting thiolate anion becomes susceptible to oxidation

Thiols have pK(a) usually around 9-10. So at neutral or acidic pH they are neutral (sulfur is protonated). But under basic conditions at pH above their pK(a) values sulfur atom is deprotonated forming thiol-anion. At this pH thiols are highly nucleophilic and easily react with electrophiles (they can be e.g. alkylated, acylated, or oxidized, etc.). So pH starts to affect the status of cysteine SH group at the values over 8-8.5.