Is there a recommendation for the number of connector mailboxes ?

My first question is are you on EmailXtender? EmailXtender has come end of life and was replaced by SourceOne. To answer your question on connection mailboxes, the more you add the more likely you will see a degraded performance. Depending on the size of your environment I would sugggest 1 mailbox connector per mail server but without knowing your environment I can't make a suggestion. I hope this helps. Take care.

Cheers.  Yes on EmailXtender still, hoping to move to Sourceone soon.  We've got approx 4000 mailboxes on a clustered exchange environment.  In total we've got 2 exchange virtual servers with 7 storage groups.