The meaning of しきり after a noun

Question

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?

Answer 1

The しきり(だ) means:

しきり【頻り】
〘形動〙同じことが何度も起こるさま。また、その程度・度合いがはなはだしいさま。
「催促がしきりだ」
「後悔することしきりだ」
▹動詞「しき（頻）る」の連用形から。
（from 明鏡国語辞典）

The しきり is a na-adjective. It comes from the verb しきる(頻る), meaning "to do something incessantly".

It can follow a noun, Verb+こと, or Noun+が, like this:

反省することしきりだ。
感心頻りであった。
～との声がしきりだ。

～しきり(だ) sounds pretty literary and you wouldn't use it in casual speech.

As an aside, you'd more often see 「しきりに」"frequently", as in:

しきりに背後を気にする