Burton has an excellent analysis of this abrogation case on pages 186-188 of his book. He argues against the abrogation claim. Here are the highlights: 1.
The commands in 73:1-4 are in singular form, directed to the Prophet (PBUH), while the commands in 73:20 are in plural form, directed to other Muslims as well. Therefore, the addressee is different.2.
If 73:20 came to reduce a burden, it reduces a burden on the Muslims so it would be 'abrogating' a tradition, not a command in another verse.3.
The stated practice in 73:20 is heavier than what 73:1-4 would necessitate, so the lightening of the burden may have been addressing an exaggeration that took place that is not dictated by the command in 73:1-4.4.
The directives to the Prophet (PBUH) to stay the night praying continue in other, later verses. He cites5.
The entire basis of the abrogation claim is a narration of A'isha, may God be pleased with her.6.
This abrogation case is intermingled in the theological dispute about whether only the 5 prayers are required. The opinions about that are less unequivocal than what one would expect.7.
Some prominent scholars do not see this as an abrogation case, including Ka'b Al-Ahbar, Hasan Basri, and Al-Suddi.Disclaimer: The facts that are not self evident here need to be taken with caution as the source is a non-Muslim writer.