For keep ~ing, we usually use the verb 続ける which means to continue, to keep, etc.
e.g.
食べる＋続ける＝食べ続ける
勉強する＋続ける＝勉強し続ける
Depending on the context, other expression could be more appropriate than ～続ける.
～てばかりいる for example, which means doing something all the time.
食べてばかりいる
勉強してばかりいる