She must love her work or she wouldn't have kept at it all these years.

or 在这里是连词，表示"否则、要不然"，用于连接两个并列的句子，表示前句不成立时后句的情况就会发生。 wouldn't have kept 是虚拟语气结构，表示对过去情况的假设性否定，"不会(已经)坚持"的意思。