Is there a time limit for filing a case after a lawyer signs a power of attorney?

There is no time limit.

But if you are a lawyer, I suggest you pay attention to the statute of limitations. If the work is not busy and the case is not complicated, it is recommended to do a good job of filing a case within one week after receiving the case. If the work is busy or the case is complicated, it is suggested to inform the parties clearly that it takes time to sort out the materials and strive to file a case within one month.

If you are a party, I suggest you give your lawyer enough trust and give him proper time to handle the case.

In addition, please tell whether your "lawyer" is a real lawyer. If you are employed by a so-called legal service company rather than a law firm, you are basically not a lawyer.