I think it means “almost everyday”. I often see it used as a simile:
赤ちゃんのように寝る。“Sleep like a baby.” So, it might be used more figuratively, or it might just be a set expression meaning “almost everyday” or “like everyday”. Hopefully that helps.
~のように can mean ‘as’ or ‘like’, so I’d go with “almost every day” or “like every day”, as pointed out, as well as “almost on a daily basis”.
Consider:
ジムsan(lol)は日本人のように日本語を話します。Jim speaks Japanese like a Japanese.
今日は春になったように暖かいです。Today is as warm as if it had become spring.
上田さんのように走れますか。Can you run like Mr Ueda?
猫がかわいいように犬もかわいいです。Just like cats are cute, so are dogs. (Dogs are cute, just like cats),
Yes, 毎日のように means “almost evey day” or “like everyday”. The translation should be: “I” couldn’t escape from the boy’s bad friends who came over to play almost every day.