The reason actually has nothing to do with VaYelech, but with Ki-Savo.
The Gemara in Megillah 31b says that the curses in Devarim (Ki-Savo) have to be read before Rosh Hashana - so as to end the year and its curses.
We then add one Parsha as a break, so that we don't enter the new year from the curses.
We then have a practical issue how to stretch/squeeze the remainder of the Torah in before Simchat Torah. So in years with 2 "free" Shabatot between Rosh Hashana and Sukkoth (excluding Yom Kippour) we have to split Nitzavim from Vayelech. In years with only 1 free Shabbat, we read them together, before Rosh Hashana.
As to what is intrinsically special about VaYelech:
- It's the Shortest Sedra
- Most of its 30 verses talk about Moshe's upcoming death and forecasting the Yidden's behaviour.
- It has the last 2 Mitzvos:
- (612): The once-in-7-year Hakhel gathering
- (613): Writing a Sefer Torah
Not sure why we'd want to read about this twice in some years and not at all in others.