Written communication with the reviewer via PMs isn't always as effective as you may wish: it takes time from everyone's schedule and the information might not get through as you intended. Sometimes, you may not get the reply in time to make the correct decision. For example, the PM of one of our clients is located in UK, while the reviewer is in Tokyo. Obviously, we've had situations when we sent questions for the reviewer to the PM and before he could get to them, the workday in Japan was over, so the reviewer didn't get them on the same day. So we had to wait for answers to simple questions for two days.
If you clearly see that communicating through intermediaries isn't doing you and the client any good, it's time to connect with the reviewer directly. Yes, not every client will share their reviewer's contact information, but don't be afraid to ask. It's possible that their PM will happily arrange your communication with the reviewer, ridding them of the hassle and waste of time that are involved in managing your collaboration.
We were successful many times in convincing the client's PM to connect us directly with the person that reviewed our work. As a result, we saved our and the client's time and gave the linguist a real opportunity to go through the nuances that caused the argument in the first place. After such discussions, we clearly understood how to translate the text the next time around, so the reviewer would be happy. They, on the other hand, were able to accept our arguments in some cases not to correct certain terms or sentence structures, introducing mistakes instead of making the text better.
Make sure to discuss with the reviewer how you will communicate in the future. Any means will do. We use messengers, emails or phone calls, for example. Sometimes, we organize a conference call, inviting all the linguists that work on the project for the specific client. This way, recommendations and instructions from the reviewer are sure to get to everyone, and everyone is sure to have a chance to ask direct questions. If there are many participants, or you're expecting a heated discussion, it's best to set a moderator—the project PM would do perfectly, for example.