In general, a single forgery should have been reported to the bank within one year. However, since it's a series of forgeries by the same wrongdoer, the the model version of the UCC would hold the customer liable for forgeries occurring more than 30 days after the statement on which the first forgery appeared. Your signature card may reduce that time frame, but it's unlikely.
On the forgeries that your bank may be liable for, you are still entitled to raise defenses such as the customer's negligence contributed to the forgery or the customer's employee was a "trusted" employee so the customer is at least partially liable for the employee's actions.
Emphatically: No, the bank's liability is not unlimited. Depending on the circumstances, it may have no liability at all. Get your bank's lawyer involved.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.