Short answer. Not on the neglect ground alone. Article 282 makes neglect a just cause only where it is gross and habitual, and how much money the mistake cost is not what those words measure. An expensive one-off lapse may still be examined under a different ground in the same list.
What the law says
Gross and habitual neglect by the employee of his duties
Labor Code, Article 282 — Just Causes For Dismissal. Read the full provision →
The cost of the mistake is not the statutory test
This is the point that most surprises workers in your position. The article does not describe the loss at all — it describes the conduct, and it does so with two adjectives that both have to fit. Neglect must be gross, meaning the want of care was serious rather than an ordinary slip, and it must be habitual, meaning repeated. A single error can be enormously expensive and still be neither. An employer that leads with the peso figure is arguing about consequences, when the ground it has invoked asks about the character and the frequency of the neglect.
Both words have to be satisfied
Because the two adjectives are joined, showing one does not carry the ground. Careless work that has happened many times may fail the gross requirement if each instance was minor. A serious lapse that happened once may fail the habitual requirement no matter how badly it turned out. It is worth asking your employer squarely which prior incidents it is relying on to establish habituality, and whether those were ever recorded at the time. Warnings written up only after the costly incident, and backdated in substance if not in date, are the usual weak point.
Where a single costly act can still land
Article 282 lists other grounds, and a one-off act is capable of falling under them. Serious misconduct, wilful disobedience of a lawful order connected with your work, and fraud or wilful breach of the trust reposed in you are each stated without any requirement of repetition. But they carry their own thresholds — misconduct must be serious, disobedience and breach of trust must be wilful — and none of them is satisfied by an honest error. A mistake is not misconduct; the distinction between doing something badly and doing something deliberately is the line the whole article runs on.
The employer is held to the ground it chose
Find out, in writing, which cause you were actually charged with. This matters because the analysis differs sharply between them, and an employer that dismissed you for neglect cannot later re-argue the case as breach of trust once the habituality problem is pointed out. Keep the notice you were given, your performance records, and any prior warnings, together with whatever accounts for how the loss arose — a system fault, a rushed instruction or a colleague's involvement can all reframe what happened. Those documents are what a lawyer needs to assess the ground as it was pleaded.