design help for performance

I am bumping into some performance issues and am seeking help.

I have two tables A and B in a one (A) to many (B) relationship. There are
1.4 million records in table A and 44 million records in table B. In my
web application any request for a record from table A is also going to need
a count of associated records in table B. Several years ago I added
table_b_rowcount to table A in order to minimize queries on table B. And
now, as the application has grown, I am starting to having locking problems
on table A. Any change to table B requires the that table_b_rowcount be
updated on table A... The application has outgrown this solution.

So... is there a common solution to this problem?

culley