I think that the clipping happens in the first place is a known issue. In the Github issue hadley says: "I think this is a long standing problem that I'm unlikely to solve in the near future"
I think there are two ways, you can more or less solve the problem for yourself. One solution was already mentioned by @Arnaud
(but both solutions have downsides)
Add clip = "off" in the coord_map part
Add expand = c(1.1,0) in the scale_x_continuous part
I added you some example plots, where you can see the results and problems.
1. Initial version (if I run your code):

Problem: The point at (0,0) can't be seen properly.
2. Version with expand:
skydata <- data.frame(RA=c(0,180,360), Dec=c(0,10,20))
ggplot(skydata) +
geom_point(aes(RA,Dec)) +
coord_map(projection="aitoff", orientation=c(90,180,0)) +
scale_y_continuous(breaks=(-2:2)*30,limits=c(-90,90)) +
scale_x_continuous(breaks=(0:8)*45,limits=c(0,360), ,expand = c(1.1, 0), labels=c("","","","","","","","","")) +
labs(x="R.A.(°)", y="Decl. (°)",title="Map of the sky")

Looks quite nice now. x-axis got expanded to both sides, point in (0,0) now clearly visible.
But attention seems to work only with natural numbers (like expand = c(5,0)). For the 1.1 I chose in my example the plot is somehow different and the y-axis seems distorted.
3. Version with clip = "off":
skydata <- data.frame(RA=c(0,180,360), Dec=c(0,10,20))
ggplot(skydata) +
geom_point(aes(RA,Dec)) +
coord_map(projection="aitoff", clip = "off", orientation=c(90,180,0)) +
scale_y_continuous(breaks=(-2:2)*30,limits=c(-90,90)) +
scale_x_continuous(breaks=(0:8)*45,limits=c(0,360), labels=c("","","","","","","","","")) +
labs(x="R.A.(°)", y="Decl. (°)",title="Map of the sky")

This version does not expand the x-axis, but it makes sure, the point at (0,0) is not clipped off. Definitely no distortion of the y-axis. But does not look as good as the solution with expand.