I created mailbox with unlimited messages count, but messages are still being blocked.
Even if mailbox has "unlimited" parameter, delivery may be blocked because domain or subscirption limit was exceeded.
Check and adjust domain subscription limits.
Outgoing Mail Control limits and its priority:
Server wide limits:
The following limits act as the default limits, which can be overridden in each service plan and subscription. The limits do not work server-wide, but act as a template for the plans and subscriptions for which no custom limits were specified.
Define limits for particular mailbox
Define limits for particular domain
Define limtis for particular subscription
Subscription limits level has the highest priority, mailbox the lower:
Susbscirption -> Domain -> Mailbox
For example, if mailbox has "unlimited" parameter and on subscription level only 10 messages are allowed - mailbox user will not able to send more than 10 messages.