First, not sure where you're getting your data, but it's not accurate. HBD peg has held well since HF 25 when the Hive->HBD conversion operation was added. I've had bots trying to buy it at 0.99 or below off and on since the HF, with very little success (I've been lucky enough to buy a couple thousand at 0.98-0.99 range) .
If you were trading on HBD/BTC market, you might have got lucky and got some small amount at a cheaper price when BTC took a rapid dive before orders could be removed by HBD sellers (one guy mentioned he managed to buy about $40 USD worth at a better price, maybe around 0.92 USD). But trades like that are purely short term anomalies that aren't really meaningful to the overall stability of the coin.
Now on the high side, the price was around $1.20 for a substantial amount of time. But if there had been any large Hive stakeholder with a strong desire to quickly stabilize it down to $1.00, it could have been done: most just found it more profitable to slowly sell to whoever was trying to rally the price. And ultimately that buy pressure capitulated, as you can see in the graph below.
This graph shows the price of HBD since the HF. The small black arrow shows when HF25 triggered and basically put the brakes on how far HBD can rally:
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[EDIT] my arrow didn't show up but HF25 was on June 30th, killing that first spike you see (although it was already starting to die, June 30th is on the tail end of it).
Generally speaking, with current trading behavior, I think you can expect to see HBD trade anywhere between 0.99 and 1.06. If it starts to exceed that, you can expect that traders will start doing Hive->HBD traders to profit from the arbitrage opportunity. And the @hdbstabilizer puts pressure on the price in the 1.01 to 1.05 range and puts associated profits back to the decentralized hive fund. Finally, the other operation, HBD->Hive conversion, keeps price from dropping much below $1. Interest payments also add some upward pressure to the price, which encourages it to stay a percent or so above $1.