Recently I had to troubleshoot a Exchange 2013 IMAP issue with a voicemail server. It was very strange since I have not seen this behavior before. The IMAP service was running and restarting the services had no effect. Once the IMAP voicemail message is read the voicemail light on the phone should stop blinking. After some research, I noticed that the IMAP Proxy was Inactive. Commands used for this below.
This powershell command shows the state of components Exchange is using.
Get-ServerComponentState -identity yourservername
This powershell command enables IMAP Proxy.
Set-ServerComponentState -Identity yourservername -Component ImapProxy -Requester HealthAPI -State Active
After this and after IMAP caught back up, everything was working again like normal. It seems like it is always a learning experience.
Links below: