Examination of the fine structures of the component/components of the oil might provide some clues in this matter.
Certain structural features can make a compound prone to peroxide formation. Presence of ether linkages (R-O-R) in the molecule could be one example.
Ethers (diethyl ether, tetrahydrofuran etc,) have a great tendency towards peroxide formation during storage, and this can be assisted by the presence of moist air and light.