He was unable to continue his research because of illness.
Literal
Illness [because-のため] he [topic-は] research [object-を] continuing [could-not-ことができなかった].
病気のため marks illness as the cause. 研究を続けることができなかった combines the formal potential ~ことができる in its negative past form. A clean example of のため + ことができなかった for cause-and-inability.