I recently came across this sentence:
耳打ちするようにしながらもしっかり声が届くように言うホロに苦笑いしきりだが、ノーラが無防備にうなずいたことにはちょっと傷ついた。
I thought at first that しきり might be しきる, as in "do to completion", but then it would make more sense as 「しきったが」rather than 「しきりだが」. I also saw on a Chiebukuro post that as 頻り, 「後悔しきり」means to "regret one thing after another". The main character of the story does make this expression quite often at ホロ. However, I am still unsure what しきり means here.
What does this しきり mean?