Shirk al-Asghar does not remove a person from Islaam:

بـسـم الله والحـمـد لله والـصلاة والـسـلام عــلى رسـول الله، وبـعـد

Allaah تعالى said:

﴿إِنَّ اللَّـهَ لَا يَغْفِرُ أَن يُشْرَكَ بِهِ وَيَغْفِرُ مَا دُونَ ذَٰلِكَ لِمَن يَشَاءُ﴾

{Verily, Allaah forgives not that partners should be set up with him in worship, but He forgives except that (anything else) to whom He pleases} [Surah al-Nisaa’ (4): 48]

Shaikh Ibn Baaz رحمه الله said:

The one who commits Shirk al-Asghar (minor Shirk), if his good deeds outweigh (the bad deeds), it is hoped that they (the good deeds) will remain. As for the verse, then the obvious is that it refers to Shirk al-Akbar (only).

Source:

 الفوائد الجلية من دروس الشيخ ابن باز العلمية (ص 23)

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The Shaikh رحمه الله was asked: Does Shirk al-Asghar removes the person from Islaam?

Answer: Shirk al-Asghar does not remove a person from Islaam. Rather, it decreases the Imaan and negates perfect Tawheed which is required from a person.

So if a person recites (the Qur’aan) for showing off or he gives charity for showing off, then his Imaan decreases and weakens and he has incurred a sin while doing this act, but he is not judged as a Kaafir.

[Majmoo` al-Fataawa Ibn Baaz (8/394)]

Summary:

1. Only that action in which Shirk al-Asghar has happened will be effected.

2. Instead of reward, sin will be recorded for him.

3. His other good deeds will not be effected, in-shaa Allaah.

4. His Imaan will decrease and weaken.

5. His Tawheed will not be perfect.

6. He is still upon Islaam.

7. Tawbah is required from him. 

8. The person should not treat this as something insignificant, as little drops of water make the mighty ocean.