Short answer. Yes, in one specific situation. If the counter-bond is found to be or becomes insufficient and you fail to file an additional counter-bond, the attaching party may apply for a new order of attachment. Posting security once is not a permanent immunity.
What the law says
Should such counter-bond for any reason be found to be or become insufficient, and the party furnishing the same fail to file an additional counter-bond, the attaching party may apply for a new order of attachment.
Rule 57, Section 12 — Discharge of attachment upon giving counter. Read the full provision →
The security must stay adequate, not merely start adequate
When the discharge is granted, the deposit or counter-bond stands in place of the property released, and it secures payment of any judgment the attaching party may recover in the action. The rule therefore treats sufficiency as a continuing requirement rather than a one-off test passed at the start. The words be found to be or become insufficient cover two different situations: a bond that was never adequate in the first place, and one that was adequate when filed but has ceased to be so since. Both put you back at risk if you do not respond.
How a counter-bond becomes insufficient
The rule does not list the causes, and it does not need to, because it says for any reason. In practical terms the usual concerns are about the surety rather than about you. A surety may cease to be solvent, may have its authority to transact withdrawn, or may turn out to be over-committed across other bonds. The amount itself may also be overtaken if the court revisits the value on which it was originally based. None of these are matters you control, which is why the position is worth checking rather than assuming.
You get a chance to cure it first
The right to apply for a new order of attachment is not automatic. It arises only if the party furnishing the counter-bond fails to file an additional counter-bond. So the sequence built into the rule gives you an opportunity to make up the shortfall before the property is exposed again. That opportunity is only useful if you learn about the problem in time, which is a good reason to keep track of the surety's standing instead of treating the bond as finished business once the property has been released.
What a new order would mean
An application for a new order of attachment starts that process over rather than reviving the old writ automatically, and because it is an application to the court it can be opposed. Even so, the practical effect of losing at that stage is that assets are tied up a second time, after you have already paid for a bond once. Keeping the existing security sound is almost always cheaper than contesting a fresh attachment, and it avoids a second round of the same argument.