Messages get stuck in Local Delivery

Over the past few days we've had to reboot our exchange server a couple of times each day to clear out the Local Delivery queue. There are a couple of errors that seem to coincide with the issue. Errors are below. Does anyone have any idea what might be going on here?

Source: MSExchangeIS
Category: General
Event ID: 9667
failed to create a new named property for database "First Storage Group\Mailbox Store (T-1000)" because the number of named properties reached the quota limit (8192).
 User attempting to create the named property: "SYSTEM"
 Named property GUID: 00020386-0000-0000-c000-000000000046
 Named property name/id: "X-MS-General"

Source: Server ActiveSync
Category: None
Event ID: 3007
Exchange mailbox Server response timeout: Server: [] User: []. Exchange ActiveSync Server failed to communicate with the Exchange mailbox server in a timely manner. Verify that the Exchange mailbox Server is working correctly and is not overloaded.
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Hi This Might Help in your case. Microsoft always makes sure users suffer due to lazy coding guys  :) 

Rick FeeMessaging Engineer - Disaster Recovery EngineerCommented:
This could be due a few different reasons.    Here is quick article you should read. 
Shreedhar EtteCommented:

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