How can I use できない and しまう？ I'd like to apologize for not being able to do something


I'd like to apologize for not being able to do xyz.

Rather than just saying 「すみません、何々ができません。」, could I say something like:

> 何々ができなくてしまいます。

Or is しまう always used with a positive te-form verb?




Firstly, I'm not very knowledgeable about grammar so I might be talking about
a different usage of the same しまう.

しまう is used when you have done something unintentionally or unwillingly. For
example, from the sentence:

> 花瓶を壊してしまう。

you can tell that the person didn't break the vase on purpose, whereas in

> 花瓶を壊した。

you can't really tell the person's intention.

Now for your example, できなくてしまいます is できない + しまう. できる/できない is about your
capability of doing something. When you're capable of something, you
_intentionally_ do whatever you're capable of. Therefore, it doesn't make much
sense to talk about something you can't do, but can do at the same time.

That being said, できてしまう is used, I think mostly in novels, when you want to
say that you are capable of doing something that you are not willing to do.
For example,

> 諦めることができてしまう。

means that you are able to give up, even though you are unwilling to do so.

