This phrase means "many times". It is interchangeable with 何回も. 一度もVません indicates that the action has never taken place, not even once.
弟は 何度も 重い 病気を した ことが あります。
My younger brother has gone through serious diseases many times.
母は まだ 一度も 弟を しかった ことが ありません。
My mother has never scolded my younger brother.
Lesson 15-7「こどもが 十人も います。」
They have / There are as many as ten children.