How do you deal with functional managers in a matrix organization?

Then is time to talk with her/him and just in case is needed to escalate to something above her/him. Just talking about my personal case we include in our project charter the governance model we will follow as simple as a pyramid where you visually can see the percentage of issues/risks that we intended to be solved into each step, the frecuency of meetings, people must participate in those meetings and the level of escalation. In our case we manage escalation showing that we are trying to help people to find the time to participate in all needed for the project, not as a mean to punish somebody. Because for us the project charter is the "contract" with all our clients then when it is agreed it must not be broken.

Think carefully about going over a functional manager's head.
-Does he/she have some influence in the organization
-Do his/her objections have real value
-What is the culture of the organization? does it allow going around someone to make your point?
-Is there another way to achieve success, and eliminate the barrier? Perhaps the sponsor first is better

Sergio, I agree with you and I know that it's time to talk to the functional manager or to escalate to top management. Anyway I don't know whether you have come across situations where even the top management cannot do anything to persuade the functional manager (I guess this happens only in public enterprises). I had a similar situation several years ago, so I approached the top management and I was told to wait until the functional manager retires in few years.

I fully understand that the motive of the project team is to help people rather than to punish somebody, but in my experience sometimes it doesn't work as expected.

I appreciate your feedback and comments on this.

I worked a lot in public sector. Is not about public sector. I faced the same in private sector. What I stated is what I do. Top management are the owner of all projects inside the organization. They are accountable for projects then if they do not take action it does mean the project has not value and there is not reason for project existence. Is a matter of governance. What I stated is what I did and I still doing when I face this type of situations.

Thanks Sergio, for letting me know.

Agree with Shivanjali and Drake. Need to understand other sponsors standpoint and create a win-win proposition, also thereafter if required approach to leadership of functional manager.

No problem. I deal with this type of situations each year. Beyond what I have written above my attitude is: no matter the amount of effort we do from kickoff to any type of thing "by the book" we do I have to sell the initiative to all people I need to be engaged. I am not a seller but because the positions I worked in the past I was training in several selling methods. The method that helps me a lot in this type of situations is "Solution Seliing" or "SPIN Selling". On the other side, sometimes I have to request to put inside the annual objectives of people that I have detected as key stakeholders something related to the initiatives and that was the only way to keep them moving.