[Exim] inbox file becomes locked while downloading mail

Hello,

This is my first post here and I am complete newbie, so please bear with
me... :)

I'm not even sure I'm writing to the correct mailing list! Perhaps what I'll
write below isn't even Exim's problem...

I (or, to be more exact, my hosting providers - 3 of them) have following
problem with Exim 4.24:

- my mailbox generates ~500mb/day incoming (NOT outgoing - I'm not a
spammer, you know..) mail transfer;

- while I'm downloading it (sometimes it's taking quite long time, as you
can imagine), inbox file becomes locked (quite logical thing) and no
new mail is delivered;

- after download I experience what I really don't want to: those messages
which were received by the server, but not delivered aren't delivered for
a few hours, days, or even lost forever. The 'record' time between 'recei-
ved' and 'delivery-date' headers was somewhat around 50 hours;

- and yes, I've searched FAQ;

- and no, I've not read O'Reilly or UIT Cambridge books :)

Hosting companies are trying to help, but don't know how.

Is this a known bug (well, not a bug - a MONSTER!)? And what do you can
propose for a poor fella like me?

If this isn't Exim's problem, please do answer privately, not harassing
anybody in this nice group. If this is in the FAQ, answers like RTFM are
accepted as well... Just tell me please where to look... :)

Thank you, thank you very much!

Arunas
an@???