Halruaan magical shields went up, making teleportation and scrying impossible and clouding most divination magic into chaotic uselessness.
When the Spellplague hit, many Halruaans died, magic briefly "went wild", and structures collapsed. In-flight effects failed and gravity took over, active magics turned chaotic, and so on. At the same time, many wizards went insane or got brain-burned or were killed when caught in their own spells going chaotic. A lot of the surviving Halruaans assumed the realm was under attack and cast or activated all of their appropriate "rainy day" defenses, so more shields went up, many of them twisted or going wild as time passed.
Halruaa was effectively cut off from the rest of Faerûn, caught in mid-dimensional segueing between Abeir and Toril. Not the entire country as a neat whole unit, but bits and pieces of it in a very localized fashion. This in turn meant more wild magic and the leakage of other magics from elsewhere through it, and more defensive spellcasting, and an increasing "no go zone" from the point of view of those nearby in Toril. So it doesn't so much "blink" as it disappears into/behind impenetrable mists of tangled magic, for a time.
To emerge with many structures devastated, the populace scattered, weary, and wary . . . and even more determined to be isolationalist. All the magical chaos has shattered Halruaan society, in that their "usual ways" and attitudes have been swept away, and every family is questioning their status quo (laws, customs, reliance on magic, assumptions about their place in the world). There was much loss of life, a lot of fear and paranoia, and so as the result of the return of the Weave, a lot of hard work went into variants and "improvements" on the guards and wards spell, placing it permanently in various dwellings (most new Halruaan dwellings look like fortresses, and are readily defensible) and in "rings" around the land (food gardens, ponds, orchards, etc.) immediately surrounding those dwellings. A favorite Halruaan tactic is to have prowling guardian creatures hiding inside thick conjured fogs/mists, so intruders can't see what's approaching and/or watching them.
Halruaa no longer has any formal contact with the outside world, so many folk elsewhere in Faerûn may think it is a fallen, abandoned land. And it does have numerous wild magic "zones" along its borders, moved and kept there by the strongest surviving Halruaan spellcasters, as a deterrent to outsiders. Right now, Halruaa is definitely in "leave us alone, nothing to see here, so move along, right away" mode.