[Dovecot] Issue with Mavericks Mail Client

We run a dovecot mailserver. One of the clients I use is a Mac Laptop. Recently I upgraded from Mountain Lion (10.8) to Mavericks (10.9). Under 10.8 it worked fine. On 10.9 it syncs up when I invoke the client, but after a while stops getting updates.

Most of my mail clients are on Linux (thunderbird) or Android (K9) and I admit that several run against my very large INBOX simultaneously. The one of the 10.9 Mac laptop is the only one with this issue.

Is there something known about the new 10.9 Mail client on the Mac that would lose sync against dovecot?