The problem was that 3 out 3 of my recent hosts had quite similar bug: unpredictable delay in mail deliveries and overall incoming mail loss. Now, the problem seems to contrentrate on Exim 4.24 and I think it occurs while I'm downloading mail from the server (this can take sometimes an hour!). Mailbox becomes locked, new mail isn't delivered and starts wandering inside the server for hours, days, or as it looks, forever... (headers are showing considerable time betwen "received" and "delivery-time") This is what _I_ think - all _YOUR_ thoughts are welcome!
Have anyone of you had this kind of problems/complains from the customers and if yes, how you solved them? 4.24 isn't the latest Exim release (4.30 is), perhaps it's the only buggy one?
It is natural that the inbox file gets locked when you check mail. If it is still locked when Exim attempts to append newly-arrived message to the inbox file, the delivery is deferred but the message should stay in the retry queue.
The actual delivery time depends a lot on the retry settings. I think the way Exim calculates the retry time may contribute to the delays (I believe it is not calculated for individual messages but for domains).