If you lose an opportunity, lose gracefully. Maintain your professionalism, no matter how you lose. Be respectful of the prospective client’s decision, and be respectful of your competitor.
At some point, your dream client is going to change their partner again. When they do, they are going to base their own decision about whether they allow you to compete for their business again on what they remember about how you compete (as well as how good of a job you have done nurturing the relationships you have built with members of their team).
When you lose an opportunity, it is fine to argue your case, as long as you do so politely and professionally. It is also okay to ask your dream client to reconsider their decision, especially if there are issues surrounding their decision that may harm them (in fact, you are obligated to, if you really care about them). But you can’t be argumentative while you are pleading your case.
There are boundaries that you do not want to cross, lest you prove to your prospective client that they made the correct decision by choosing your competitor.
You don’t want anything you say or write to come across as a personal attack on the person or people who made the decision. You don’t want to attack their integrity or their ability to make a good decision. You don’t ever want to plead for their business because you were personally counting on winning their business (don’t laugh, I’ve seen this done).
Your ability to lose with professionalism and grace is what allows you to maintain the relationships you need so that you can compete and win the next time. And never be so desperate for any one deal that you can’t be professional no matter what happens.