Has Saudi Arabia ever been invaded?
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Saudi Arabia is a very new country, having been founded in 1932. Yet it has been invaded: Saudi–Yemeni War (1934)
"The Saudi Government has tried all pacific means through diplomatic channels to come to an agreement with the Imam of the Yemen, but he obstinately persists in his aggressive policy by occupying our highlands in Tehama, oppressing their inhabitants, and eradicating all who do not surrender to his rule.
With the British as sponsors, and later the US as a protector, Saudi Arabia has been relatively safe from its lessor neighbors. It also maintains a fairly substantial military.
So your opening statement is shown to be false.
If you mean "Why was Arabia never invaded?", the premise is false: The north-western part, was invaded and conquered by the Romans.
The Lakhmids controlled the north-eastern part of Arabia circa 300 AD; this region was later invaded by the Persians.
The entire region was invaded and conquered by the Ottomans.
Ottoman Arabia ~1914.
If you carefully restrict the definition of "Arabia", one can find regions which were very loosely ruled from outside, and which were, perhaps, never invaded. Any location in the deep desert would probably qualify under this methodology.
According to Arab sources, the Christian Ethiopian kingdom, and/or their client state in Yemen, invaded central Arabia in 570 on what was likely (if it happened) a punitive expidition. This is noteworthy because the army supposedly brought some African elephants with them, so the locals called this The Year of the Elephant.
This in turn is noteworthy because The Prophet Mohammed was (traditionally) born there in the Year of the Elephant.
As for why such things haven't happened more often, you probably ought to look at what resources are there worth fighting over. Its a desert. Until Oil was discovered there in the last 100 years or so, there wouldn't be much reason to go into the interior of Arabia if you weren't wanted.
Saudi Arabia has been invaded as recently as the first Gulf War war by Saddam's forces.
The area invaded is a bit odd. Internationally both Kuwait and Saudi Arabia have recognized borders, but some of the area along their borders is jointly administrated by them. It's not really disputed, they just never invested the effort to come up with a better solution.