In 1998, a client sent a letter (I have a copy) to the bank with instructions to make future plan investments into the XYZ Fund. The bank moved current money into the fund, but did not make any future investments into the fund. The client recently realized that his instructions weren't followed.

Aside from the fact that the client should have picked up on this 11 years ago, doesn't the bank bear some responsibility? The earnings loss is significant.

Was this a plan that provided for participant direction of investments? Or was is a plan where the bank was the fiduciary managing the investments and the participant or employer indicated a preference?
Of course there may be some liability. If under the terms of the trust documents the bank was to have followed the investment direction given, the bank would be liable to make up losses which occurred as a result of that failure. However, generally a statute of limitations would limit recovery to 3 years from the date of discovery of the failure.
Your client will be put in the uncomfortable position of having to admit that he didn't look at the bank's performance reports for 10 years, which may impact his credibility.

Check the U.S. Supreme Court's decision in the DeWolff case. It had some similarity of facts.